At one point, the White House officials said, Mr. Priebus asked Mr. McCabe if he could say publicly that “senior intelligence officials” had informed him that the Times article was inaccurate, and he was told that he could. Mr. Priebus did that in an interview on Sunday.

The F.B.I. on Friday declined to provide its account of those conversations and declined to comment on Mr. Trump’s Twitter statements.

The executive editor of The Times, Dean Baquet, said on Friday that “The Times had numerous sources confirming this story.”

“Attacking it does not make it less true,” Mr. Baquet said.

An F.B.I. official confirmed on Thursday night that the White House had asked last week for the bureau’s help disputing the story, and that senior F.B.I. officials had rejected the request, citing the continuing investigation into Russian efforts to affect the election.

The official declined to say whether White House officials had reached out directly to Mr. Comey, Mr. McCabe or others. The official said the White House had reached out to American intelligence agencies in the hopes of enlisting their help.

Tension between the F.B.I. and the White House is not unheard-of. President Bill Clinton had an icy relationship with his F.B.I. director, Louis J. Freeh, whose agents investigated the president and his associates for years. But it is very unusual for a president to openly criticize the entire bureau.