Mr. Wray and Deputy Attorney General Rod J. Rosenstein had already tried unsuccessfully this week to persuade the White House to stop the release of the memo, and Thomas O’Connor, the president of the F.B.I. Agents Association, issued a statement on Thursday supporting Mr. Wray. It thanked the director for “standing shoulder to shoulder with the men and women of the F.B.I.” and came a day after the bureau itself strongly condemned the push for the memo’s release.
Despite the White House worries about his unhappiness at the prospect of the document’s release, Mr. Wray, who has kept a relatively low profile since taking over the F.B.I. in August, was unlikely to resign over this issue, people familiar with his thinking said.
Speaker Paul D. Ryan, speaking Thursday to reporters at the Republicans’ annual policy retreat in West Virginia, rejected criticisms of the memo and offered a full-throated defense of the document.
“This memo is not an indictment of the F.B.I., of the Department of Justice. It does not impugn the Mueller investigation or the deputy attorney general,” he said, referring to Robert S. Mueller III, the special counsel investigating the Russian election meddling and whether Mr. Trump obstructed justice.
Instead, Mr. Ryan said, the memo was the product of Congress employing oversight of the executive branch.
Mr. Trump has told the people close to him that he believes the memo, which the White House confirmed he had read, makes the case that law enforcement officials acted inappropriately and with bias in the early days of the Russia investigation. He has spent less time talking about it in the White House than some of his supporters have, however.
But people close to Mr. Trump who have been told of the memo’s contents, both inside and outside the White House, conceded that the document was not likely to deliver on those expectations.
Republicans who have seen the three-and-a-half page memo say it makes a case that political bias infected a key action in the early stages of the Russia investigation. It contends that officials from the F.B.I. and Justice Department may have misled a Foreign Intelligence Surveillance Court judge when they sought a warrant to spy on the former Trump campaign adviser, Carter Page, in October 2016.
The memo says the officials relied in part on information handed over by a former British intelligence officer, Christopher Steele, without adequately explaining to the judge that the research was paid for by the Democratic National Committee and Hillary Clinton’s presidential campaign, according to people who have read the document. And it says the material from Mr. Steele was not vetted.
Law enforcement officials described Mr. Steele not as an investigator funded by Democrats but as a reliable source to the bureau who had provided helpful information about corruption in FIFA, soccer’s global governing body, according to two people familiar with the warrant application.
The memo is also said to take note of the role of several senior law enforcement officials, including Mr. Rosenstein and Andrew G. McCabe, the former deputy director of the F.B.I. who quit under pressure this week. Both men were said to be involved at various points in authorizing applications for the surveillance that Republicans say was flawed.
The document was primarily written by Kashyap Patel, a committee staff member for Representative Devin Nunes, Republican of California and the chairman of the Intelligence Committee.
Democrats who have seen it say the Republican document amounts to a risky attempt to construct a narrative to undercut the Russia investigation. They say it relies on cherry-picked facts and disregards key context.
Representative Steve Cohen, Democrat of Tennessee, called the document “a banal, inferior, non-shocking, insubstantial memo.”
“Obviously, they wanted to make a point and claim prejudice against President Trump,” he said on Thursday. “When you read the Democratic side, the minority report, it is pretty obvious that all the information that could be before the judge was there.”
Mr. Page had been on the authorities’ radar for years. He had visited Moscow in July 2016 and was preparing to return there that December when investigators obtained the warrant.
Tensions ran high on Thursday among lawmakers, with the House and Senate Democratic leaders calling on Mr. Ryan to remove Mr. Nunes from his chairmanship and one senior Republican senator cautioning that his House colleagues should slow down their push to release the document.
Republicans and Democrats on the Intelligence Committee spent the day arguing over charges by Democrats that the Republicans had made “material changes” to the memo after the committee voted to release it but before it was transmitted to the White House for review. Representative Adam B. Schiff of California, the top Democrat on the Intelligence Committee, wrote in a letter late Wednesday that the committee needed to restart the process and vote on the revised memo.
Republicans quickly countered that Mr. Schiff was “complaining about minor edits” and said their vote was “absolutely procedurally sound.” But a senior Democratic official familiar with the changes said the Democrats had found five material differences in the versions of the memo, including one that the official described as an apparent effort to water down the Republican findings. There were six separate changes to grammar or word choice, the official said. It was not immediately clear whether the changes were related to those requested by the F.B.I.
In a sharply worded letter of her own, Representative Nancy Pelosi of California, the House Democratic leader, called on Mr. Nunes to be removed as the Intelligence Committee’s chairman.
“Congressman Nunes’s deliberately dishonest actions make him unfit to serve as chairman, and he must be removed immediately from this position,” she wrote, adding, “The integrity of the House is at stake.”
Mr. Ryan dismissed the idea during his afternoon news conference, saying that the Democrats were merely “playing politics.”
Mr. Ryan — speaking in part to his Republican colleagues — urged readers of the memo not to “draw lines” between the material discussed in it and the work or character of Mr. Mueller or Mr. Rosenstein.
The plea was not universally embraced.
Representative Jeff Duncan, Republican of South Carolina, who has been among the memo’s most vocal advocates, wrote on Twitter that the F.B.I. was right to have “grave concerns” about the release “as it will shake the organization down to its core.”
At least three prominent Republican senators — John Thune of South Dakota, the No. 3 in the Senate; Lindsey Graham of South Carolina; and Jeff Flake of Arizona — urged caution. Mr. Flake, in a joint statement with Senator Chris Coons, Democrat of Delaware, said releasing the memo “risks undermining U.S. intelligence-gathering efforts, politicizing Congress’ oversight role and eroding confidence in our institutions of government.”
Mr. Thune said he thought that the Senate Intelligence Committee and its Republican chairman, Senator Richard M. Burr of North Carolina, should be allowed to see the document before its release. And he called for a Democratic memo rebutting the Republican document to be shown to the public at the same time.
Speaking to reporters on Thursday night at a Charleston, S.C., hotel, Mr. Graham expressed concerns over the handling of the memo, which he, like other senators, has not read.
“I’m the chair of the Judiciary Crime Subcommittee with oversight of the F.B.I.,” he said. “I don’t particularly appreciate having to read about it in the paper.”
He suggested that Mr. Nunes’s document was not the best avenue for informing the public.
“A partisan memo,” he said, “is going to lead to another partisan memo.”
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