The memo is their latest salvo. Led by Mr. Nunes, the House Intelligence Committee is pivoting from examining Russia’s election meddling to instead investigating F.B.I. and Justice Department officials connected to the inquiry, putting them — with Mr. Ryan’s clear blessing — at the forefront of the broader pushback.

Republicans are pushing the narrative that a cabal of politically biased law enforcement officials set out to sabotage Mr. Trump. And they are portraying a dossier written by Christopher Steele, a former British intelligence agent, which laid out unverified claims that Russia had compromised Mr. Trump and was conspiring with him, as the fountainhead of the Russia investigation. That assertion disregards unrelated evidence that Russia sought to influence the election and the pattern of contacts between Russians and Mr. Trump’s associates.

Mr. Nunes’s three-and-a-half page memo bolsters conservatives’ story line. According to people who have read it, the memo centers on a fall 2016 application for a wiretap order targeting Carter Page, a onetime Trump campaign official who had visited Moscow that June and was preparing to return there in December. The memo is said to criticize law enforcement officials for including information provided by Mr. Steele in the application without adequately explaining to the judge that Democrats financed Mr. Steele’s research.

Democrats have pushed back. Representative Adam B. Schiff, the top Democrat on the Intelligence Committee, who has seen the underlying classified materials on which the memo is based, has said the memo contains both inaccurate assertions and material omissions to misleadingly impugn law enforcement officials. Other people familiar with it say, for example, that Mr. Steele’s information was only one thread in a tapestry of evidence from various sources that the memo ignored, exaggerating its relative importance.

Democrats on the committee produced their own classified memo that they said pointed out and explained inaccuracies in the Republican memo and filled in the missing context. But on Monday, the committee voted along party lines to make the Republican memo public and rejected a request to simultaneously make public the Democrats’ rebuttal.