(CNN) The House Intelligence Committee voted unanimously Monday evening to make public the Democratic memo rebutting GOP allegations that the FBI abused surveillance laws, the committee's top Democrat said, a move that will put the issue back on President Donald Trump's desk this week.

The classified memo from Rep. Adam Schiff, the top Democrat on the House Intelligence Committee, is written to push back against the central allegations of the Republican memo from Intelligence Chairman Devin Nunes. Nunes' memo was released Friday and alleges the FBI abused the FISA process in obtaining a surveillance warrant on former Trump campaign foreign policy adviser Carter Page.

Schiff told reporters Monday evening that the committee also agreed to send the Democratic memo to the FBI and Justice Department to play a role in the Executive Branch approval process.

Schiff and other Democrats charge that Nunes' memo is inaccurate and misleading, and the 10-page Schiff memo goes point-by-point to counter the charges in the Nunes memo. Schiff has said he has given his memo to the Justice Department for review.

RELATED: Read the disputed memo here

The GOP-led House Intelligence Committee blocked the release of the Democratic memo at last week's committee meeting, saying members had just been presented with the document, instead moving forward with the four-page Nunes memo that now has been declassified after Trump agreed to its release Friday.

The panel did, however, agree last week to let the full House review the Schiff memo in a classified setting. Republicans leaving the closed-door meeting on Monday said they support its release, which is now in the hands of the White House.

The process for publicly releasing the Schiff memo is the same as the Nunes document: The President will have five days to decide whether to allow the document to be made public or object to its release. If the President objects, the House Intelligence Committee could send the matter to the full House to debate in closed session and vote on whether to make the memo public.

Following Monday's vote, White House press secretary Sarah Sanders said the administration will follow the same procedure for reviewing the Schiff memo as it did the Nunes one last week. But she stopped short of saying the White House would declassify the new memo.

The classified memo is expected to be taken by courier to the White House Monday evening, the official said, setting into motion the five-day review period. The official did not say whether the decision would be made before Friday, but suggested it could be.

One Florida Republican who is helping run the Russia investigation, Rep. Tom Rooney, said he though there wouldn't be much in the Schiff memo to redact.

Schiff told reporters he thought that Republicans felt they had to vote to release the Democratic memo after blocking it last week -- adding that he thought it would also be very difficult for the White House to object to its release.

But Schiff said he's concerned the White House will make "political redactions" to the memo before releasing it, and not just to protect sensitive information, and that's why he asked the Justice Department and FBI to play a role vetting the document. Schiff says they have already provided the memo to DOJ and FBI, but have not gotten a response yet.

Monday's meeting also renewed the committee's fight over the role that the White House played with the Nunes memo, which Trump said "vindicates" him on Sunday.

Rep. Mike Quigley, an Illinois Democrat, pressed Nunes during the meeting on whether he had coordinated with the White House in any aspect of the memo, just as he had one week prior when Nunes did not respond to his questions about staff involvement with the White House on the memo.

Nunes read a statement at the meeting saying that the White House was not involved with the "drafting" of the Republican memo. But that did not satisfy Democrats, as Schiff said it was a "lawyerly" response that does not address whether the White House coordinated in other ways surrounding the creation of the memo.

Trump tweeted about both Schiff and Nunes on Monday morning, slamming the top Democrat on the Intelligence Committee and praising the Republican chairman, although he didn't address Schiff's memo specifically.

"Little Adam Schiff, who is desperate to run for higher office, is one of the biggest liars and leakers in Washington, right up there with Comey, Warner, Brennan and Clapper! Adam leaves closed committee hearings to illegally leak confidential information. Must be stopped!" Trump tweeted.

"Representative Devin Nunes, a man of tremendous courage and grit, may someday be recognized as a Great American Hero for what he has exposed and what he has had to endure!" he tweeted two hours later.

Schiff responded to Trump with a tweet of his own.

"Mr. President, I see you've had a busy morning of 'Executive Time.' Instead of tweeting false smears, the American people would appreciate it if you turned off the TV and helped solve the funding crisis, protected Dreamers or...really anything else," he tweeted.