According to a law enforcement official briefed on the investigation, Mr. Comey met with Mr. Priebus at the White House on Feb. 8 — a week before Mr. Comey said Mr. Trump cornered him in the Oval Office and asked him to end an investigation into Mr. Trump’s former national security adviser, Michael T. Flynn. In Mr. Comey’s meeting with Mr. Priebus, Mr. Comey told Mr. Priebus about a Justice Department policy that largely bars discussions between White House officials and the F.B.I. about continuing investigations in order to prevent political meddling — or at least the appearance of it — in the bureau’s work, according to the law enforcement official.

It is not clear whether Mr. Priebus ever relayed that message to the president. Mr. Trump’s Republican allies — including the House speaker, Paul D. Ryan — have said that Mr. Trump may have asked Mr. Comey to end the investigation because he was a new president who did not understand the subtleties of how the commander in chief should interact with the F.B.I.

Mr. Priebus may also be able to help prosecutors verify crucial details about Mr. Trump’s interactions with Mr. Comey. According to testimony Mr. Comey provided to Congress, Mr. Priebus knows that Mr. Comey had the one-on-one encounter with Mr. Trump on Feb. 14, when Mr. Comey has said Mr. Trump asked him to end the Flynn investigation. Mr. Trump has said that the meeting did not occur and that he did not ask Mr. Comey to end the inquiry.

Mr. Comey said in his testimony to Congress that on Feb. 14, Mr. Trump had Mr. Priebus, the attorney general, the vice president and other senior administration officials removed from the Oval Office after a counterterrorism briefing.

“The president began by saying Flynn hadn’t done anything wrong in speaking with the Russians, but he had to let him go because he had misled the vice president,” Mr. Comey said.

“The president then made a long series of comments about the problem with leaks of classified information — a concern I shared and still share. After he had spoken for a few minutes about leaks, Reince Priebus leaned in through the door by the grandfather clock and I could see a group of people waiting behind him. The president waved at him to close the door, saying he would be done shortly. The door closed.”

Right after the door closed, Mr. Comey said, Mr. Trump asked him to end the Flynn investigation.

Mr. Trump and his lawyers have tried to cast the search warrant served on Mr. Manafort as an unusual measure and an abuse of power. The president said he was surprised to learn about the search, saying it was something federal authorities “very seldom” do. John Dowd, a lawyer for Mr. Trump, said the search was similar to tactics used in Russia.