But White House chief counsel Don McGahn later said it could not be released in its current state "because the memorandum contains numerous properly classified and especially sensitive passages".
Trump said earlier Friday he planned to release the memo.
Trump weighed in with a tweet on Saturday.
However, the Democrats knew this, they - they packed their memo full of sources and methods.
Democrats warn this does not just amount to a double standard, but also reflects a pattern of attempts by the President to frustrate the investigation because he has something to hide.
"If Schiff (or anyone else) is going to claim that it is Grassley's intent to undermine the Mueller probe, they should back it up with actual evidence or retract it and apologize for questioning the motives of their colleagues without any basis whatsoever", Foy said.
Critics of Mueller's probe have used the GOP memo, and other sources, to argue that the inquiry is baseless and spurred by political animus to Trump.
Because of this deception, Grassley and Graham "are referring Christopher Steele to the Department of Justice for investigation of potential violation (s) of 18 U.S.C. § 1001", which could lead to a criminal indictment.
House Democratic Leader Nancy Pelosi was less measured, saying the White House move is "part of a risky and desperate pattern of cover-up on the part of the president".
The top Democrat on the committee is criticizing Trump for treating the two documents differently.
House Intelligence Committee Chairman Devin Nunes, R-Calif., strides to a GOP conference joined at right by Rep. Peter King, R-N.Y., also a member of the Intelligence Committee, at the Capitol in Washington, Tuesday, Feb. 6, 2018. The GOP memo notes how the department obtained a secret Foreign Intelligence Surveillance Court order to wiretap Page.
However, the White House decision was criticised by Democrats - with House minority leader Nancy Pelosi claiming it proves that the release of the initial memo was a "blatantly political move". Republicans backed the release, but several said they thought it should be redacted. Democrats say the court was informed that a former British spy, Christopher Steele, who assembled the dossier, was politically motivated.
Schiff's comments come after the White House's decision last week not to publish the Democratic rebuttal document.
In response, a memo was prepared by Democrats that reportedly contests and further details the claims made by Republicans. Some Republicans likewise disagreed with the conclusions being drawn from that document.
Schiff, who has traded bitter Twitter messages with the president after Trump called him one of "the biggest liars and leakers" in Washington, warned this week that Trump might call for "political edits" meant to erase embarrassing parts of the memo, not information related to national security.
In the wake of the House Intelligence Committee's release of a GOP-crafted memo alleging surveillance abuses by the Department of Justice, Rep. Adam Schiff, D-California, is defending the Federal Bureau of Investigation for its conduct in seeking a Foreign Intelligence Surveillance Act (FISA) warrant against former Trump campaign adviser Carter Page. "If they really wanted to get it out, they'd be down there all day yesterday redacting it, getting it back over to the White House so that the public can know what's in it". Let's see what they've got.