 -- The Senate's top Democrat is calling on President Donald Trump to officially approve the release of a Democratic memorandum said to counter claims made in the memo he declassified Friday at the request of Republicans on the House Intelligence Committee.

In a letter to the president Sunday, New York Sen. Charles Schumer said the American people need to see the memo from the committee's top Democrat -- Rep. Adam Schiff of California -- to decide for themselves.

"I strongly urge you to sanction the public release of Ranking Member Adam Schiff’s memorandum that was recently made available to all members of the House of Representatives as soon as possible," Schumer said in the letter. "I believe it is a matter of fundamental fairness that the American people be allowed to see both sides of the argument and make their own judgments.

"A refusal to release the Schiff memo in light of the fact that Chairman Devin Nunes’ memo was released and is based on the same underlying documents will confirm the American people’s worst fears that the release of Chairman Nunes’ memo was only intended to undermine Special Counsel Bob Mueller’s investigation," Schumer's letter said.

White House principal deputy press secretary Raj Shah told CNN Friday, "I think the president would be inclined to release the Democratic memo should it come to us and should it be reviewed and gone through the same process and if national security and legal equities review it and say it doesn't challenge sources and methods, the information in it."

On Friday, Schiff said Democrats would seek a committee vote Monday to make their memo public by sending it to Trump but said that, unlike committee Republicans, "we will ask the relevant agencies to propose any necessary redactions to protect any sources and methods not already disclosed by Chairman Nunes’ document."

On Sunday, asked whether he thinks Nunes coordinated the GOP memo release with the White House, Schiff said: “I think it's very possible his staff worked with the White House and coordinated the whole effort with the White House.”

Speaking with ABC News Chief Anchor George Stephanopoulos on “This Week,” Schiff was asked whether he thought any coordination could be viewed as an attempt to obstruct justice in the Russia investigation.

Schiff replied, "I don't know whether members of Congress can be part of an obstruction case -- but the president’s use of this, the president’s decision, for example, ‘I’m going to release the memo even though the FBI says it’s inaccurate, even though the Department of Justice says it’s reckless’ -- that could be evidence of the president’s intent to interfere with the investigation."

Nunes, a Republican from California, denied any coordination on Fox News Friday.

A committee Republican, Rep. Will Hurd of Texas, also appearing on "This Week," explained why he voted against releasing the Democratic memo at the same time as the GOP memo.

"There was information there that I did believe led to the erosion of national security. There were some references to ongoing intelligence operations. I believe they're working through that...," Hurd said.

At the same time, Hurd and other Republicans on the House Intelligence Committee appearing on the Sunday shows disagreed with the president's tweet Saturday saying the GOP memo "totally vindicates 'Trump' in probe. But the Russian Witch Hunt goes on and on."

On Fox News Sunday, Rep. Chris Stewart, a Utah Republican said, "I think it would be a mistake for anyone to suggest that the special counsel shouldn't complete his work. I support his work, I want him to finish it. I hope he finishes it as quickly as possible. This memo has frankly nothing at all to do with a special counsel."

Another Republican, Rep. Trey Gowdy of South Carolina, said on the CBS program "Face The Nation" that Deputy Attorney General Rod Rosenstein should not lose his job over the alleged Justice Department and FBI abuses in seeking a surveillance warrant on Trump campaign adviser Carter Page.

"It doesn't mean someone should lose their job, it doesn't mean they're corrupt," Gowdy said. "But it also doesn't mean Congress is not legitimate in asking these questions, because I think we are."

Asked on CNN's "State of the Union" whether he thinks the GOP memo provides a pretext for firing Rosenstein or Mueller, Rep. Brad Wenstrup of Ohio said, "No I don’t," adding, "I support the Mueller investigation."

Also appearing on CNN, Senate Democratic Whip Dick Durbin was asked what Democrats will do if Trump were to try to fire either or both men.

"Listen, this would be an extreme event and one that I say with some caution could create a constitutional crisis in this country," Durbin said. "The question at that moment is whether or not the majority Republicans in the House and the Senate will stand up for the rule of law and the Constitution if the president takes that extreme position."

ABC News" Alexander Mallin and Benjamin Siegel contributed to this report.