President Trump said on Thursday that he would name the Fox News personality Jeanine Pirro, whose false statements about the 2020 election were part of a lawsuit against the network, the interim U.S. attorney for Washington, hours after he was forced to pull his first choice.

Selecting Ms. Pirro, the former Republican district attorney of Westchester County, N.Y., resolves a thorny dilemma for the president, who said hours earlier that he would withdraw his nomination to permanently install the interim U.S. attorney, Ed Martin, under pressure from Senate Republicans.

“During her time in office, Jeanine was a powerful crusader for victims of crime,” the president wrote on social media in announcing the pick, listing her background in law enforcement. He added, “She is in a class by herself.”

The move raised legal questions. Mr. Trump appeared to be relying on an aggressive interpretation of his appointment powers, and his installation of Ms. Pirro could face a legal challenge. A ruling striking down her appointment could disrupt criminal cases brought on her authority, while one upholding it would expand Mr. Trump’s power to bypass the Senate.

Ms. Pirro, 73, has known the president for decades, has earned his trust and would provide him with a reliable line into one of the country’s most important federal prosecutors offices in the Justice Department.

Ms. Pirro has not held a law enforcement job in the two decades since she stepped down as district attorney to pursue bids for higher office, including an ill-fated run against Hillary Clinton for Senate before the 2006 election.