Former New York mayor Rudolph W. Giuliani and two other former federal prosecutors joined President Trump’s legal team Thursday following weeks of turbulence and struggles to find attorneys who would agree to represent the president in the ongoing federal probe into Russian election interference.

The reshuffling comes at a particularly tense juncture for Trump, who aides said is increasingly frustrated by special counsel Robert S. Mueller III’s investigation and with the senior officials at the Justice Department.

The entry of Giuliani, an experienced attorney with a combative reputation, immediately raises questions about how Trump will engage with Mueller and the leadership at Justice. Some Trump advisers are concerned that the president could use his ­executive authority to close or diminish the special counsel probe, which has spawned a parallel investigation in New York targeting his personal attorney.

“I’m doing it because I hope we can negotiate an end to this for the good of the country and because I have high regard for the president and for Bob Mueller,” Giuliani said in an interview Thursday.

Trump said in a statement that Giuliani “wants to get this matter quickly resolved.”

In recent days, the president has been regularly venting and speculating to aides about his legal status and the expected timeline for the Russia investigation to end, according to associates briefed on the discussions.

Trump also loudly and repeatedly complained to several advisers earlier this week that former FBI director James B. Comey, former deputy FBI director Andrew McCabe and former Democratic presidential nominee Hillary Clinton, among others, should be charged with crimes for misdeeds alleged by Republicans, the associates said.

Although White House officials said Thursday that Trump has not called Justice Department officials or taken any formal action, the persistent grousing has made some advisers anxious, according to two people close to the president. A publicity tour by Comey to promote his book critical of Trump, “A Higher Loyalty,” has attracted particular attention from the president, who has disparaged Comey publicly and privately.

Trump also complained this week about Supreme Court Justice Neil M. Gorsuch, saying the judge had proved too liberal in recent cases, according to administration officials who heard about the complaints. Associates said he was incensed that Gorsuch had voted against the administration on an immigration case and said it renewed his doubts that Gorsuch would be a reliable conservative. One top Trump adviser played down the comments as unhappiness with Gorsuch’s decision rather than with Gorsuch broadly.

Giuliani, 73, brings a familiarity with several of the legal fronts that Trump is navigating. He is a former associate attorney general and a former U.S. attorney for the Southern District of New York, which is the office overseeing an investigation of Trump’s personal attorney, Michael Cohen.

Trump counsel Jay Sekulow said Thursday that former federal prosecutors Jane Serene Raskin and Marty Raskin, a couple who manage a Florida-based law firm, have also agreed to join the legal team.

Giuliani is certain to come under intense scrutiny for his role. His own pre-election activities two years ago have been the subject of criticism from Democrats, especially television interviews in which he suggested he had sources providing him inside information about the FBI’s investigation of Clinton’s private email server when she was secretary of state.

A Justice Department Inspector General report on the department’s handling of the Clinton investigations is expected to be released in coming weeks and will probably include results of leak investigations regarding the Clinton probe.

Numerous other challenges face the attorneys who will work alongside Sekulow and counsel Ty Cobb — who have functioned as Trump’s legal nucleus for weeks following the resignation of John Dowd, a legal veteran and the team’s former leader. Dowd stepped down in March amid clashes over strategy and whether Trump should sit for a voluntary interview with Mueller. The legal team has often been beset by infighting.

“The big question is, how’s he going to play with everybody else?” said a lawyer involved with the investigation who was not authorized to speak publicly. “Will he be combative Rudy, or will he play well with Mueller’s team? Will he try to walk . . . back from the brink and answer the big question, which is whether the president will sit for an interview? And will Trump listen to him?”

Giuliani declined to say whether Trump has made a final decision on whether to sit for an interview with federal investigators. Trump has been mulling it for weeks, moving away from the idea after the home, offices and hotel room of Cohen were raided this month. Trump reacted angrily, calling it “disgraceful.”

“It’s too early for me to say that,” Giuliani replied, when asked whether a Trump interview is unlikely to happen.

Giuliani also declined to discuss whether Deputy Attorney General Rod J. Rosenstein, who has been under fire from conservatives and oversees the Russia probe, could be fired by the president in the coming weeks.

“I’m not involved in anything about those issues. My advice on Mueller has been this: He should be allowed to do his job. He’s entitled to do his job.”

Giuliani said he formalized his decision in recent days, including over dinner last week at Trump’s Mar-a-Lago resort in Florida. Giuliani and Trump spoke Thursday about the legal plan moving forward, along with Sekulow, whom he has known for years and called a friend. He added that he and Cobb also spoke, on Wednesday.

Giuliani — who will take a leave from his law firm, Greenberg Traurig, and is in the midst of a divorce from his third wife — said he would spend a “great deal of time” in Washington working with Trump but would continue to live in New York. He has been frequently been seen holding court at the Trump International Hotel in Washington, dining and drinking with friends and browsing for gourmet cigars.

Trump had considered Giuliani for attorney general and has said in recent weeks he needs a New York-based attorney. Many leading white-collar lawyers, such as former solicitor general Theodore Olson, have declined Trump’s entreaties, often citing conflicts or expressing unease about the high-profile case.

Trump is also known to be a difficult client who does not always listen to his attorneys’ advice, according to lawyers who know him. And Giuliani, once a top adviser, grew frustrated with his treatment during the transition and had receded from the inner circle.

As he has closely monitored cable-news programs chronicling his presidency and the Mueller probe, Trump has swatted away the notion that he cannot attract prominent attorneys. He has also spoken about his desire for a bolstered team and wondered aloud about the damage that Cohen’s legal proceedings could bring, according to the associates briefed on the discussions, who requested anonymity to talk about them.

Giuliani’s arrival is part of a broader shift in Trump’s inner circle toward the core allies and brusque and brutal style that defined his outsider presidential campaign and his business career. Beyond Mueller, aides said everyone and everything around Trump feels liable to become a target for his wrath as he grapples with difficult issues at home and abroad, in Syria and North Korea.

“What we’ve been seeing with the president is that he is picking A-level people that he knows are experienced but also know him well,” said Trump ally Christopher Ruddy, the president and CEO of Newsmax Media, a conservative outlet. “One of the problems in the first year was that people didn’t work out because they didn’t know him and they didn’t have experience for the position.”

Carol D. Leonnig contributed to this report.