Democrats also say Republicans misrepresented the words of Andrew G. McCabe, the former deputy director of the Federal Bureau of Investigation, when they said he told the committee late a year ago that the agency would not have sought a wiretap of Page without Steele's dossier of information.
Schiff disputed the president's claims that Democrats acted in bad faith when crafting their memo, saying "the hypocrisy of this just kind of reaches out and grabs you by the throat".
"It was not clear what the president meant by "(and more)".
But congressional Democrats and Republicans, including House Speaker Paul Ryan of Wisconsin and Rep. Trey Gowdy of SC, who helped draft the GOP memo, have said it shouldn't be used to undermine the special counsel.
The White House says the Justice Department had identified portions of the memo that "would create especially significant concerns for the national security and law enforcement interests" of the country. Trump has repeatedly denied any collusion.
Trump claimed the original memo "totally vindicated" him in his role in attempts to thwart the special counsel's investigation of the matter but investigators and even Republicans say it shows more illegal involvement in it.
Nunes, for his part, said it was "no surprise" that the Schiff memo wasn't released, given its lack of redactions.
Real Madrid 5 v Real Sociedad 2 - story of the match
But his form has been erratic this season and, amid talk Real want to sign Neymar in the summer, a move back to the Premier League may be in the offing.
Democrats and US intelligence officials had strongly disputed the GOP memo's accuracy before and after its release.
Trump declassified the GOP memo over the objections of Rosenstein and Wray.
House Minority Leader Nancy Pelosi, D-Calif., was less measured than Schiff, saying the White House move is "part of a risky and desperate pattern of cover-up on the part of the president".
He is a political operative and author of a second Trump-Russia dossier.
There are also suspicions the White House is working with Nunes to politicize the committee's oversight of the investigation into whether the Trump campaign colluded with a Russian effort to interfere in the 2016 election or whether the President obstructed justice. (The memo doesn't directly quote McCabe's comments, which came in a closed-door Intelligence Committee hearing, but instead paraphrases him.) The memo also seemed to undermine its own claims by pointing out that the Russian Federation investigation began months before the Steele dossier was used in the FISA application.
"Told them to re-do and send back in proper form!" the president said in a tweet.
Democrats on the intelligence committee complained the Republicans' four-page memo cherry-picked facts and explained events out of context and was thus not accurate.
"We actually want the Democratic memo out", he said.
It does appear that the Democratic memo contains details that could be reasonably said to endanger national security. Trump authorised its release anyway.