WASHINGTON — As Republicans on the House Intelligence Committee backed away on Sunday from President Trump’s claim that a newly released memo vindicates him in the Russia investigation, Democrats pressed for the release of their own classified rebuttal, with a vote expected on Monday on whether to make it public.

The memo that the panel’s Republicans released on Friday claims that federal law enforcement officials abused their powers to spy on a former Trump campaign official. In the days since its release, members of the two parties have clashed sharply over its import: While some Republicans say it shows evidence of bias in the Russia inquiry from the start, Democrats have denounced it as a misleading tactic to undermine the investigation and protect Mr. Trump.

Republicans on the committee voted against releasing the Democratic rebuttal memo last Monday at the same time they chose to initiate the release of their own three-and-a-half-page document. But several of those Republicans, as well as the House speaker, Paul D. Ryan, have indicated that they now favor releasing the Democratic memo, as long as it has been scrubbed of sensitive national security information.

Democrats have said their 10-page memo corrects mischaracterizations by the Republicans and adds crucial context to actions by the F.B.I. and the Justice Department in obtaining a secret Foreign Intelligence Surveillance Court order to wiretap the former Trump aide, Carter Page.