Accompanied by a letter from the White House, the Democrat-drafted memo was sent back to the House Intelligence Committee for changes.
In the letter, White House Counsel Donald McGahn said, "Although the President is inclined to declassify the February 5th Memorandum, because the Memorandum contains numerous properly classified and especially sensitive passages, he is unable to do so at this time."
The House panel voted unanimously on Monday to release the 10-page Democrat-drafted memo, which is expected to lay out a point-by-point rebuttal of the assertions in the previous Republican-drafted one.
According to the Republican-drafted memo, which Trump approved for release last week, a number of top US law enforcement leaders abused their power by inappropriately obtaining a surveillance warrant on Carter Page, a foreign policy adviser to the Trump presidential campaign until September 2016.
Democratic lawmakers have called the memo misleading and part of an effort to undermine Special Counsel Robert Mueller's ongoing probe.
The Federal Bureau of Investigation (FBI), which objects to the release of the Republican-drafted memo, said in a statement last week that it has "grave concerns about material omissions of fact that fundamentally impact the memo's accuracy."