Democrats said it was aimed at derailing ongoing investigations into the Trump campaign's links with Russia.
The document has glaring holes, detractors say, and the FBI itself said it had "grave concerns" over its accuracy.
Page says he never cut any political deals with the Kremlin and says there was nothing illegal in his interactions with Russian officials.
They said such action could result in a constitutional crisis not seen since the 1970s when then President Richard Nixon gave orders to fire justice officials involved in the Watergate scandal.
Right now, he genuinely doesn't know the answer to that question.
On Friday, hours after the release of the Nunes memo, FBI director Christopher Wray sought to bolster FBI agents and analysts with a memo of his own.
On Saturday, Nadler circulated a memo to House Democrats disputing the conclusions of the Nunes memo and arguing that Page was a lawful target of surveillance, according to NBC News.
"A lot of people should be ashamed of themselves", he said following the memo's declassification.
In its application to the FISA court, the FBI had also cited extensively from a Yahoo News article dated September 23, 2016, about Mr Page's trip to Moscow. "In this case, the director's oral account of the memos is no substitute for the written hard copy", Boasberg wrote.
US President Donald Trump commented on the Republican memo, on the role of the FBI and the Justice Department in the investigation into Russia's alleged interference in the 2016 US presidential election. Comey's statements, he said, did not come close enough to matching the specificity of his memos.
Attorney General Jeff Sessions, criticized by Trump for recusing himself from the Russia investigation, offered praise for Rosenstein as well as the department's No 3 official Rachel Brand on Friday, saying they "represent the kind of quality and leadership that we want in the department". Whatever they do is fine.
"I think it's a disgrace, what's going on in this country", he said.
On Friday, President Donald Trump approved the declassification of a highly controversial memo, spearheaded by Nunes, that alleges FBI abuses of its surveillance authority.
The memo alleges a surveillance warrant was obtained and renewed on a former Trump campaign adviser, Page, with information from an individual with an anti-Trump agenda.
"The memo gives us too little information to make a conclusion about whether the government abused the surveillance laws", he concludes.
The memo has become a flashpoint in the bitter dispute between Republicans and Democrats over investigations into whether Russia colluded with the Trump campaign in the 2016 election.
"Don't worry, 100%" Trump told Rep. Duncan Hunter on Tuesday after the lawmaker urged him to release the document. A statement released by ranking member Rep. Adam Schiff and other House Intelligence Committee Democrats suggests there is a connection, but Nunes chose to leave that out.
Seeking to defuse the conflict, Republican House Speaker Paul Ryan backed the release of a Democratic counterpoint memo if the Republican document were made public.
The Department of Justice's response is due February 14.
Trump and his Republican allies have been ramping up their war on the Mueller investigation since December, when former national security adviser Michael Flynn pleaded guilty to lying to FBI agents about his Russia contacts.