The outlines of the memo were widely detailed in news reports in recent days. Several details from the complete memo show that it reflects a line of attack circulating for weeks in conservative media outlets, which have been amplifying a narrative that the Russia investigation is the illegitimate handiwork of a cabal of senior Justice Department and F.B.I. officials who were biased against President Trump and set out to sabotage him.
One of its chief accusations centers on investigators’ inclusion in the FISA warrant application of material from a former British spy, Christopher Steele. Mr. Steele was researching possible ties between Russia’s election interference and Trump associates, but the application did not explain that he was financed by the Democratic National Committee and lawyers for Hillary Clinton’s campaign.
But a Democratic memo written to rebut the Republican document says that the F.B.I. was more forthcoming with the surveillance court than the Republicans say. The F.B.I. told the court that the information it received from Mr. Steele was politically motivated, although the agency did not specifically identify the information as financed by Democrats, according to two people familiar with the Democratic memo.
It is not clear to what extent the FISA application hinges on the material provided by Mr. Steele. In December 2017, the Republican memo said, Andrew G. McCabe, then the deputy director of the F.B.I., told the House Intelligence Committee that no surveillance would have been sought without Mr. Steele’s information.
But the people familiar with the Democratic memo said that Republicans had distorted what Mr. McCabe told the intelligence committee about the importance of the information from Mr. Steele. Mr. McCabe presented the material as part of a constellation of compelling evidence that raised serious suspicions about Mr. Page, the two people said. The evidence included contacts Mr. Page had in 2013 with a Russian intelligence operative.
Mr. Page’s contacts with the Russian operative led to an investigation of Mr. Page that year, including a wiretap on him, another person familiar with the matter said.
Mr. McCabe told the committee that the decision to seek a FISA warrant was also prompted by Russian attempts to target Mr. Papadopoulos, a trip Mr. Page took to Moscow in July 2016 and the Russian hacking of Democratic emails that appeared to be aimed at harming the presidential campaign of Hillary Clinton, the two people familiar with the Democratic memo said
The Democratic memo also says that when the F.B.I. returned to court to renew the wiretap on Mr. Page, bureau officials told the judge that the agency had cut ties with Mr. Steele because he was talking to reporters about the investigation. The judge extended the warrant anyway.
The Republicans’ assertion that investigators were not forthcoming about Mr. Steele is “potentially problematic,” said David Kris, a FISA expert and former head of the Justice Department’s National Security Division in the first term of the Obama administration.
If the warrant applications did disclose that Mr. Steele’s research was funded by people who were opposed to Mr. Trump’s campaign, even if it did not name the D.N.C. or the Clinton campaign, then the applications “would be fine,” he said, and the author of the memo and those who backed its release are trying to mislead the American people.
“To me, that appears to be the lens through which we should evaluate the honesty, decency, and integrity of the two sides here,” Mr. Kris said. “Not having seen the FISA applications, my money is on D.O.J. and the F.B.I., but presumably time will tell.”
Among the handful of details revealed by the publication of the memo was that the application also cited a September 2016 article published by Yahoo News. Written by the veteran investigative reporter Michael Isikoff, it cited unnamed sources saying that government investigators were scrutinizing Mr. Page’s ties to Russia.
Mr. Steele was later revealed to be a source for the article, and the memo suggests that law enforcement officials’ inclusion of it in their warrant application means they were using the same source twice but presenting it as separate sources.
“This article does not corroborate the Steele dossier because it is derived from information leaked by Steele himself to Yahoo News,” the memo said, underlining the assertion.
But it is unlikely that such an article would have been submitted to the court for the purpose of corroborating that a suspect was an agent of a foreign power, said Mr. Kris.
“The idea that they would cite a newspaper article as affirmative evidence of information contained in the article strikes me as very far-fetched,” he said. “It is much more likely that they would include an article to show that the investigation had become public, and that the target therefore might take steps to destroy evidence or cover his tracks.”
In an extraordinary move, the president declassified the identities of the people who had authorized the warrant. Republican committee staff members said the initial FISA warrant for surveillance of Mr. Page was approved by James B. Comey, the former F.B.I. director, and Sally Q. Yates, then the deputy attorney general. The date of the original application was Oct. 21, 2016.
The warrant was renewed three times, meaning Mr. Page was under surveillance for about a year. At various points in renewals of the warrant, required every 90 days, other law enforcement officials who signed off included Rod J. Rosenstein, the deputy attorney general; Dana J. Boente, now the general counsel of the F.B.I.; and Andrew G. McCabe, the former F.B.I. deputy director who resigned under pressure this week.
Mr. McCabe has been a frequent target of Republicans and of the president. Mr. Trump is also said to be unhappy with Mr. Rosenstein, who appointed Mr. Mueller as special counsel to oversee the Russia investigation.
Asked at the White House on Friday whether he would fire Mr. Rosenstein, the president cocked his head suggestively and said: “You figure that one out.”
Pressed on whether he had confidence in Mr. Rosenstein, Mr. Trump would not answer. Also on Friday, Attorney General Jeff Sessions said in a statement that he would evaluate the Republican’s criticism.
“I am determined that we will fully and fairly ascertain the truth,” he said.
The F.B.I., which had publicly clashed with the president over the memo’s release, had so far held its fire.
The memo has set off partisan fury in Congress and protests within the executive branch. Law enforcement officials have warned that they have concerns that it jeopardizes sensitive national security information.
Led by Representative Devin Nunes of California, the chairman of the Intelligence Committee, Republicans have portrayed the memo as revealing a scandalous abuse of surveillance powers by the executive branch as it launched the investigation into Russia’s interference in the 2016 election and ties to the Trump campaign.
“The committee has discovered serious violations of the public trust, and the American people have a right to know when officials in crucial institutions are abusing their authority for political purposes,” Mr. Nunes said in a statement, portraying the memo as recounting an “alarming series of events” in which intelligence and law enforcement agencies were “exploited to target one group on behalf of another.”
The memo also highlights Bruce Ohr, then an associate deputy attorney general, whose wife worked as a contractor with FusionGPS, the opposition research firm that hired Mr. Steele.
Mr. Ohr’s wife, Nellie Ohr, worked on contract for Fusion in 2016 doing translations of Russian media reports and other open-source research. Her role was relatively minor, a person familiar with her effort said. Ms. Ohr was not fully briefed on the work that Fusion was doing with Mr. Steele’s research, the person said.
Ms. Ohr’s background was in open-source intelligence — information that is publicly available — and she worked previously at the Open Source Center at the Central Intelligence Agency. The center does not handle classified information, and Ms. Ohr would not have had access to highly classified secrets or programs during her time there.
The memo also notes that the FISA application mentions Mr. Papadopoulos, who pleaded guilty last year to lying to the F.B.I. about his contacts with people connected to the Russian government. The memo said there is no evidence Mr. Papadopoulos conspired with Mr. Page.
Top officials and investigators at the F.B.I. and Justice Department have “politicized the sacred investigative process,” Mr. Trump said earlier on Friday.
Mr. Page was on the radar of intelligence agencies for years when Mr. Trump named him to be one of his foreign policy advisers in 2016. He had visited Moscow in July 2016 and was preparing to return there that December when investigators obtained the warrant. White House officials have described Mr. Page as a gadfly who had been “put on notice” by the campaign and whom Mr. Trump did not know.