WASHINGTON—White House attorneys are examining whether two loans totaling more than $500 million to Jared Kushner’s family business may have violated any criminal laws or federal ethics regulations, according to a letter from a federal ethics agency made public Monday.

The Office of Government Ethics told a Democratic lawmaker in the letter that the White House is probing whether a $184 million loan from the real-estate arm of Apollo Global Management LLC and a $325 million loan from Citigroup Inc. may have run afoul of the…