In a letter to the House Intelligence Committee, White House Counsel Donald McGahn said Mr Trump was “inclined” to declassify the document, but he could not because of “numerous properly classified and especially sensitive passages”. Mr McGahn wrote that the President would consider releasing a revised version.
Earlier in the day, Mr Trump told reporters that the Democrats' memo was going to be released “soon”.
The document in question emerged out of a protracted dispute over another memorandum, compiled by Republicans on the intelligence panel, which questioned the “legitimacy and legality” of the FBI and the Justice Department’s application to surveil former Trump campaign aide Carter Page.
In that case, Mr Trump overruled warnings about the consequences of exposing sensitive information.
After Republicans voted to declassify the memo, Mr Trump moved to make it public despite a senior justice department attorney warning that doing so would be “extraordinarily reckless” and the FBI releasing a rare statement highlighting its “grave concerns about material omissions of fact that fundamentally impact the memo’s accuracy”.
The top Democrat on the House Intelligence Committee called out those divergent responses.
“After ignoring urging of FBI & DOJ not to release misleading Nunes memo because it omits material facts, @POTUS now expresses concerns over sharing precisely those facts with public and seeks to send it back to the same Majority that produced the flawed Nunes memo to begin with,” California Democrat Adam Nunes said on Twitter.
Mr Trump has trumpeted the Republican memo as evidence of abuse that corroborates his frequent accusations that a probe of potential linkages between his presidential campaign and the Russian government is unfounded and compromised by a partisan agenda.
But Democrats have assailed the memo as an incomplete accounting that omits key information in an effort to distract from the Russia investigation. They argue their memo in response provides the full picture.
“We think this will help inform the public of the many distortions and inaccuracies in the majority memo,” Rep Adam Schiff of California, Mr Nunes said after the panel voted to release the Democrats' memo.