VIDEO - Comey Wrote Memo Saying Trump Urged Him to Drop Flynn Investigation: Sources - NBC News

Michael Flynn Carlos Barria / Reuters file

"Quite simply put, sir, you cannot stop the men and women of FBI from doing the right thing, protecting the American people and upholding the Constitution," McCabe said in response to a question from Sen. Marco Rubio, R-Florida.

In response to another question, McCabe said that the FBI was responsible for securing Comey's files and electronic devices and that he was confident that congressional overseers would have access to them.

Rep. Jason Chaffetz, R-Utah, chairman of the Committee on Oversight and Government Reform, said he would quickly seek to get his hands on the memo.

"We are drafting the necessary paperwork to get the memo, so we will find out in a hurry if it's out there," Chaffetz told NBC News, adding that if the memo exists and accurately recorded the conversation, "that seems like an extraordinary use of influence to try to shut down an investigation being done by the FBI."

Chaffetz tweeted later: "I have my subpoena pen ready."

All of the Democratic members of Chaffetz's committee and the House Judiciary Committee sent a letter to the committees' chairmen demanding an investigation into whether Trump and other top officials "are engaged in an ongoing conspiracy to obstruct" FBI, Justice Department and congressional investigations.

AshLee Strong, a spokeswoman for House Speaker Paul Ryan, R-Wisconsin, said: "We need to have all the facts, and it is appropriate for the House Oversight Committee to request this memo."

Senate Democratic leader Chuck Schumer of New York said in a floor speech that the disclosure further calls into question "the independence of our nation's highest law enforcement agencies."

"In a week full of revelation after revelation, on a day when we thought things couldn't get any worse, they have," Schumer said. "Our nation is being tested in unprecedented ways. I say to all my colleagues in the Senate: History is watching."

House Democratic leader Nancy Pelosi of California said Democrats plan to demand a vote on Wednesday to appoint an independent commission to investigate Trump's alleged ties to Russia. She said Democrats also plan to introduce legislation to appoint an independent counsel "to get the facts free of President Trump's meddling."

"With each passing day, the President's actions give greater and greater urgency to the need for a full and independent investigation of the Trump-Russia connection," Pelosi said in a statement.

Pence and other senior U.S. officials have said the firing of Comey on May 9 was unrelated to the FBI's investigation of alleged ties between Russia and Trump's presidential campaign.

Trump later tweeted that because he is so active, "it is not possible for my surrogates to stand at [a] podium with perfect accuracy" and represent the White House's line of thinking, appearing to discredit his press office and administration officials.