WASHINGTON (Reuters) - A U.S. House of Representatives committee voted unanimously on Monday to approve the release of a memo that Democrats say will rebut a contentious Republican memo alleging FBI bias against President Donald Trump .

The vote will send the memo to the White House as soon as Monday night, giving Trump until Friday to decide whether to allow its release.

If he declines, after approving the release of the Republican memo despite strong objections by the Federal Bureau of Investigation , it could set up an angry dispute pitting the White House and many of Trumps fellow Republicans in Congress against Democrats, law enforcement and intelligence agencies.

A week ago, Republicans, who control a majority on the committee, joined together to block the release of the Democrats memo and approve the Republican memo, despite unanimous Democratic opposition.

But Republican committee members said on Monday they were comfortable with releasing the Democratic document now that it had been reviewed by House members.

The Republican memo accused senior FBI and Justice Department officials of not revealing that portions of a dossier used in seeking a court warrant to eavesdrop on former Trump campaign aide Carter Page were partly paid for by Democrats.

Trump allowed its release to the public last Friday.

Democrats said the Republican memo was intended to undermine Special Counsel Robert Muellers criminal probe into possible collusion between Moscow and the Trump campaign.

The dispute, an extraordinary breach between the White House and law enforcement, also deepened partisan rancor over congressional investigations of Russia and the 2016 U.S. election, prompting concern about lawmakers ability to produce unbiased reports.

House intelligence is one of three congressional committees looking into the matter, along with Mueller.

Russia denies trying to influence the election. Trump denies collusion between his campaign and Moscow.

Trump took to Twitter on Saturday to say the memo vindicated him, and used another tweet on Monday to accuse Representative Adam Schiff, the top House Intelligence Committee Democrat, of leaking confidential material. Schiff responded by warning Trump against tweeting false smears.

The White House said it was open to releasing the Democratic memo once it goes through a security review.

Democrats worried that Trump might try to use the Republican memo to make the case for firing Mueller or Rod Rosenstein, the No. 2 official at Justice, who is overseeing the Russia probe and signed off on at least one warrant application for Page.

(Additional reporting by Doina Chiacu, Makini Brice, Steve Holland and Jonathan Landay; Editing by Alistair Bell and Peter Cooney)