No one has been charged in Sergeant Melgar’s death, which a military medical examiner ruled to be “a homicide by asphyxiation,” or strangulation, said three military officials briefed on the autopsy results. The two Navy SEALs, who have not been identified, were flown out of Mali shortly after the episode and were placed on administrative leave.

The biggest unanswered question is why Sergeant Melgar was killed. “N.C.I.S. does not discuss the details of ongoing investigations,” Ed Buice, the agency’s spokesman, said in an email, confirming that his service had taken over the case on Sept. 25.

Neither the Army nor the military’s Africa Command issued a statement about Sergeant Melgar’s death, not even after investigators changed their description of the two SEALs from “witnesses” to “persons of interest,” meaning the authorities were trying to determine what the commandos knew about the death and if they were involved.

The uncertainty has left soldiers in the tight-knit Green Beret community to speculate wildly about any number of possible motives, from whether it was a personal dispute among housemates gone horribly wrong to whether Sergeant Melgar had stumbled upon some illicit activity the SEALs were involved in, and they silenced him, according to interviews with troops and their families. Other officials briefed on the inquiry said they had heard no suggestion that the Navy commandos had been doing anything illegal.

When contacted separately by telephone on Saturday, Sergeant Melgar’s widow, Michelle, and his brother, Shawn, declined to comment.

Lawmakers have criticized top officers and Pentagon officials for offering a shifting timeline of the events in the Niger attack, and for failing to respond with timely, accurate information about the American military’s role on the continent at a time when President Trump has loosened restrictions on the armed forces to intensify attacks against the Islamic State and Al Qaeda around the world.

Sergeant Melgar, a graduate of Texas Tech University who joined the Army in 2012, was assigned to the 3rd Special Forces Group, based at Fort Bragg, N.C., the same unit whose soldiers were attacked by a much larger and heavily armed group of Islamic State fighters near the border between Niger and Mali on Oct. 4.

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According to military officials, Sergeant Melgar was part of a small team in Bamako assigned to help provide intelligence about Islamic militancies in Mali to the United States ambassador there, Paul A. Folmsbee, to protect American personnel against attacks. The sergeant also helped assess which Malian Army troops might be trained and equipped to build a counterterrorism force.

Sergeant Melgar, a native of Lubbock, Tex., was about four months into what military officials said was a six-month tour in Mali, and was living with three other American Special Operations troops in a house provided by the American Embassy.

Two of those housemates were members of the Navy’s SEAL Team 6, which has over the past decade carried out kill-or-capture missions in Libya, Yemen, Afghanistan, Iraq and Somalia, as well as the one that killed bin Laden in Abbottabad, Pakistan, in 2011.

According to two senior American military officials, the two SEAL commandos were in Mali at the request of Mr. Folmsbee in a previously undisclosed and highly unusual clandestine mission to support French and Malian counterterrorism forces battling Al Qaeda’s branch in North and West Africa, known as Al Qaeda in the Islamic Maghreb, as well as smaller cells aligned with Al Qaeda or the Islamic State. The Americans helped provide intelligence for missions, and had participated in at least two such operations in Mali this year before Sergeant Melgar’s death.

Much is unknown about what happened around 5 a.m. on June 4 in the team house. The initial reports to Sergeant Melgar’s superiors in Germany said he had been injured while wrestling or grappling with the two Navy commandos, according to three officials who have been briefed on the investigation.

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According to one version of events, one of the SEALs put Sergeant Melgar in a chokehold. When the sergeant passed out, the commandos frantically tried to revive him. Failing that, they rushed him to an emergency clinic, where he was pronounced dead.

Spokesmen for the Africa Command, the Special Operations Command, the Defense Department and the Army and Navy investigative services declined to comment, citing the continuing investigation, or did not respond to emails and phone calls on Sunday.

A spokesman for the State Department’s Africa Bureau and Mr. Folmsbee, Nicholas A. Sadoski, directed all questions to the Pentagon. Mr. Sadoski declined to answer questions about what kind of oversight the ambassador exercised over the American military personnel in Mali, how frequently was he briefed on Special Operations missions there and when he learned about Sergeant Melgar’s death.

Why American Special Operations forces are in Mali at all is a story in a nutshell of the American military’s successes and failures in Africa.

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Mali had been one of West Africa’s most stable nations before 2012, and was held up by the Pentagon as a model partner in combating Islamic militants. But when secular Tuareg separatists began an uprising, as they had done in the past, insurgents linked to Al Qaeda took advantage of the deteriorating security situation.

When the militants surged across Mali’s northern desert in 2012, American-trained commanders of the country’s elite army units defected at a critical time, taking troops, trucks, weapons and their newfound skills to the enemy. A confidential internal review completed by the Africa Command after the debacle concluded that there were critical gaps in the American training for Malian troops and senior officers.

With Mali’s army in collapse, the rebels were pushed out by French and Chadian troops early in 2013, and the United Nations established a peacekeeping mission. But the chaos continues today. Various armed insurgents regularly attack Malian forces and the United Nations peacekeepers. To date, 149 peacekeepers have been killed in Mali, making it one of the most dangerous peacekeeping missions in the world.

And terrorists continue to mount deadly attacks, including an assault in June on a resort outside Bamako that killed at least five people.

For the 3rd Special Forces Group, the past year has served as a reminder that Africa remains a dangerous assignment. In addition to Sergeant Melgar and the four soldiers killed in Niger, one soldier committed suicide in Kenya last October and another died in a vehicle accident while on patrol in Niger in February.

Those who knew Sergeant Melgar described him as a soldier’s soldier — he deployed to Afghanistan twice on training missions between July 2014 and February 2016, according to his Army service record — and a devoted father of two sons, 13 and 15, who texted and talked via Skype multiple times a day with his wife while serving overseas.

More than four months later, his death still has many at Fort Bragg and in Lubbock reeling. An online community bulletin board in Lubbock stated: “A Melgar family representative shared that ‘Staff Sgt. Melgar did what most only dream of and excelled at every turn! His life was epic! He is missed dearly every single day.’”

Sergeant Melgar was also honored at the high school he attended in Wolfforth, Tex., Frenship High, during the homecoming football game on Oct. 6.

A final tribute awaits Sergeant Melgar: He is scheduled to be buried at Arlington National Cemetery on Nov. 20.

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And now all this nasty weather has a name.

The National Hurricane Center released its 5 p.m. advisory about 25 minutes early Saturday to call it Tropical Storm Philippe. The depression that has been soaking central and western Cuba and spreading rain and thunderstorms northward across the Florida Keys and South Florida, now has sustained winds of 40 mph.

The storm is moving north at 29 mph and the forecast cone has shifted a bit west, putting South Florida into the cone of concern. On the forecast track, the center of Philippe is predicted to move off of the northern coast of Cuba and into the Florida Straits this evening. The storm will then move across the Florida Keys or the southern tip of the Florida peninsula overnight, and across the northwestern Bahamas Sunday morning, the center said in its advisory.

The tropical storm force winds are on the east end of the storm.

While the system was still a depression Saturday afternoon, it spawned a small, brief tornado that touched down just northeast of the intersection of Bird Road and Southwest 97th Avenue in Miami.

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The coastal area from Golden Beach at the Miami-Dade/Broward county line all the way down to Craig Key was placed under Tropical Storm Watch as Tropical Depression No. 18 remains on its path to Cuba, South Florida and the Bahamas.

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Prime Minister Shinzo Abe has campaigned for a military buildup against the threat from the North, and Japan sits on a stockpile of nuclear material that could power an arsenal of 6,000 weapons. Last Sunday, he won a commanding majority in parliamentary elections, fueling his hopes of revising the nation’s pacifist Constitution.

This brutal calculus over how to respond to North Korea is taking place in a region where several nations have the material, the technology, the expertise and the money to produce nuclear weapons.

Beyond South Korea and Japan, there is already talk in Australia, Myanmar, Taiwan and Vietnam about whether it makes sense to remain nuclear-free if others arm themselves — heightening fears that North Korea could set off a chain reaction in which one nation after another feels threatened and builds the bomb.

In a recent interview, Henry A. Kissinger, one of the few nuclear strategists from the early days of the Cold War still living, said he had little doubt where things were headed.

“If they continue to have nuclear weapons,” he said of North Korea, “nuclear weapons must spread in the rest of Asia.”

“It cannot be that North Korea is the only Korean country in the world that has nuclear weapons, without the South Koreans trying to match it. Nor can it be that Japan will sit there,” he added. “So therefore we’re talking about nuclear proliferation.”

Such fears have been raised before, in Asia and elsewhere, without materializing, and the global consensus against the spread of nuclear weapons is arguably stronger than ever.

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But North Korea is testing America’s nuclear umbrella — its commitment to defend its allies with nuclear weapons if necessary — in a way no nation has in decades. Similar fears of abandonment in the face of the Soviet Union’s growing arsenal helped lead Britain and France to go nuclear in the 1950s.

President Trump, who leaves Nov. 3 for a visit to Asia, has intensified these insecurities in the region. During his presidential campaign, he spoke openly of letting Japan and South Korea build nuclear arms even as he argued they should pay more to support the American military bases there.

“There is going to be a point at which we just can’t do this anymore,” he told The New York Times in March 2016. Events, he insisted, were pushing both nations toward their own nuclear arsenals anyway.

Mr. Trump has not raised that possibility in public since taking office. But he has rattled the region by engaging in bellicose rhetoric against North Korea and dismissing talks as a “waste of time.”

In Seoul and Tokyo, many have already concluded that North Korea will keep its nuclear arsenal, because the cost of stopping it will be too great — and they are weighing their options.

Capability to Build the Bomb

Long before North Korea detonated its first nuclear device, several of its neighbors secretly explored going nuclear themselves.

Japan briefly considered building a “defensive” nuclear arsenal in the 1960s despite its pacifist Constitution. South Korea twice pursued the bomb in the 1970s and 1980s, and twice backed down under American pressure. Even Taiwan ran a covert nuclear program before the United States shut it down.

Today, there is no question that both South Korea and Japan have the material and expertise to build a weapon.

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All that is stopping them is political sentiment and the risk of international sanctions. Both nations signed the Nuclear Nonproliferation Treaty, but it is unclear how severely other countries would punish two of the world’s largest economies for violating the agreement.

South Korea has 24 nuclear reactors and a huge stockpile of spent fuel from which it can extract plutonium — enough for more than 4,300 bombs, according to a 2015 paper by Charles D. Ferguson, president of the Federation of American Scientists.

Japan once pledged never to stockpile more nuclear fuel than it can burn off. But it has never completed the necessary recycling and has 10 tons of plutonium stored domestically and another 37 tons overseas.

“We keep reminding the Japanese of their pledge,” said Ernest J. Moniz, chief executive of the Nuclear Threat Initiative and an energy secretary in the Obama administration, noting that it would take years if not decades for Japan to consume its fissile material because almost all its nuclear plants have remained offline since the 2011 Fukushima accident.

China, in particular, has objected to Japan’s stockpile, warning that its traditional rival is so advanced technologically that it could use the material to quickly build a large arsenal.

Analysts often describe Japan as a “de facto” nuclear state, capable of building a weapon within a year or two. “Building a physical device is not that difficult anymore,” said Tatsujiro Suzuki, former deputy chairman of the Japan Atomic Energy Commission.

Japan already possesses long-range missile technology, he added, but would need some time to develop more sophisticated communications and control systems.

South Korea may be even further along, with a fleet of advanced missiles that carry conventional warheads. In 2004, the government disclosed that its scientists had dabbled in reprocessing and enriching nuclear material without first informing the International Atomic Energy Agency as required by treaty.

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“If we decide to stand on our own feet and put our resources together, we can build nuclear weapons in six months,” said Suh Kune-yull, a professor of nuclear engineering at Seoul National University. “The question is whether the president has the political will.”

In Seoul, a Rising Call for Arms

President Moon Jae-in has been firm in his opposition to nuclear weapons. He insists that building them or reintroducing American ones to South Korea would make it even more difficult to persuade North Korea to scrap its own.

Though Mr. Moon has received high approval ratings since his election in May, his view is increasingly a minority one.

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Calls for nuclear armament used to be dismissed as chatter from South Korea’s nationalist fringe. Not anymore. Now people often complain that South Korea cannot depend on the United States, its protector of seven decades.

The opposition Liberty Korea party called on the United States to reintroduce tactical nuclear weapons to South Korea in August after the North tested an intercontinental ballistic missile that appeared capable of reaching the mainland United States.

“If the U.N. Security Council can’t rein in North Korea with its sanctions, we will have no option but to withdraw from the Nonproliferation Treaty,” Won Yoo-chul, a party leader, said in September.

Given the failure of sanctions, threats and negotiations to stop North Korea, South Koreans are increasingly convinced the North will never give up its nuclear weapons. But they also oppose risking a war with a military solution.

Most believe the Trump administration, despite its tough talk, will ultimately acquiesce, perhaps settling for a freeze that allows the North to keep a small arsenal. And many fear that would mean giving the North the ultimate blackmail tool — and a way to keep the United States at bay.

“The reason North Korea is developing a hydrogen bomb and intercontinental ballistic missiles is not to go to war with the United States,” said Cheong Seong-chang, an analyst at the Sejong Institute near Seoul. “It’s to stop the Americans from intervening in armed skirmishes or full-scale war on the Korean Peninsula.”

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The closer the North gets to showing it can strike the United States, the more nervous South Koreans become about being abandoned. Some have asked whether Washington will risk the destruction of an American city by intervening, for example, if the North attempts to occupy a border island, as its soldiers have practiced.

For many in South Korea, the solution is a homegrown nuclear deterrent.

“If we don’t respond with our own nuclear deterrence of some kind, our people will live like nuclear hostages of North Korea,” said Cheon Seong-whun, a former presidential secretary for security strategy.

With nuclear weapons of its own, the South would gain leverage and could force North Korea back to the bargaining table, where the two sides could whittle down their arsenals through negotiations, some hawks argue.

But given the risks of going nuclear, others say Seoul should focus on persuading Washington to redeploy tactical nuclear weapons.

“The redeployment of American tactical nuclear weapons would be the surest way” to deter North Korea, Defense Minister Song Young-moo said last month, but he added that it would be difficult to get Washington to agree to that.

In Tokyo, Cautious Debate

The discussion in Japan has been more subdued than in South Korea, no surprise after 70 years of public education about the horrors of Hiroshima and Nagasaki.

But Japan has periodically considered developing nuclear weapons every decade since the 1960s.

In 2002, a top aide to Junichiro Koizumi, the prime minister then, caused a furor by suggesting Japan might one day break with its policy of never building, possessing or allowing nuclear arms on its territory.

North Korea has reopened that question.

Shigeru Ishiba, a former defense minister seen as a potential challenger to Prime Minister Abe, has argued that Japan needs to debate its nuclear policy given the threat from North Korea.

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Mr. Abe has stopped short of calling for a re-evaluation of the country’s position on nuclear weapons. But he has increased military spending and echoed Mr. Trump’s hawkish position against the North.

Mr. Abe’s administration has already determined that nuclear weapons would not be prohibited under the Constitution if maintained only for self-defense.

The Japanese public is largely opposed to nuclear weapons with polls indicating fewer than one in 10 support nuclear armament.

But Japan’s relations with South Korea have long been strained, and if Seoul armed itself, those numbers could shift.

Some analysts say the discussion is aimed at getting additional reassurance from Washington. “We always do that when we become a little upset about the credibility of the extended U.S. deterrence,” said Narushige Michishita, a professor at the National Graduate Institute for Policy Studies in Tokyo.

Tobias Harris, a Japan analyst at Teneo Intelligence, a political risk consultancy, said Japan would rethink its position on nuclear weapons if it suspects the United States would let it down.

“We’re kind of in uncharted waters as far as this goes,” he said. “It’s hard to know exactly what the threshold is that will lead the Japanese public’s switch to flip.”

Correction: October 28, 2017

An earlier version of this article misstated the amount of plutonium Japan stores overseas. It is 37 tons, not 37 million tons.

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