".@GOPoversight is going to get the Comey memo, if it exists. I need to see it sooner rather than later. I have my subpoena pen ready," Chaffetz tweeted.
Trump asked Comey to end his investigation of Michael Flynn one day after he fired him, according to a memo written by Comey detailing their discussion. The New York Times first reported the memo Tuesday
and a source familiar with the matter confirmed the contents of the memo to CNN.
A spokeswoman for House Speaker Paul Ryan showed support for Chaffetz's push.
"We need to have all the facts, and it is appropriate for the House Oversight Committee to request this memo," Ryan spokeswoman AshLee Strong said in a statement.
The head of the Republican Study Committee, Rep. Mark Walker, said that if the report is true, then it's concerning to him.
"If that's accurate, I'm hearing that it's not -- to say that we would have some concern would be accurate, that would be troubling," Walker told CNN. "To act like it's not a concern would be remiss on my part."
Rep. Cathy McMorris Rodgers, a Washington Republican, also said the report raises questions.
"I think it's really important right now that we hear from the White House," she told CNN. "I think the White House needs to be open and transparent about whats going on, too. And I hope that we can get Comey to come up here and testify."
Leaders of the congressional investigations into Russian meddling into the US election last year are also calling on Comey to testify.
The top Democrat on the House intelligence committee, Rep. Adam Schiff, also called on Comey to testify before his panel.
"Enough is enough, Congress really needs to get to the bottom of this," Schiff said.
Sen. Lindsey Graham, chairman of a judiciary subcommittee investigating Russia, said that Comey should testify before his Senate panel about his discussions with Trump over Flynn, who resigned earlier this year.
Comey had already been invited to testify before the Senate intelligence committee Tuesday about his firing a week ago, but he declined the invitation.
"OK, well, he's got to come in and tell us why," Graham said. "We're not going to try somebody on a piece of paper."
Graham also said he would consider a special prosecutor if Comey's recounting of the meeting was accurate.
"If I thought there was inappropriate behavior by the President, sure," Graham said.
Meanwhile, Democratic leaders quickly described the actions Comey depicted in a memo as "obstruction of justice."
"If these reports are true, the President's brazen attempt to shut down the FBI's investigation of Michael Flynn is an assault on the rule of law that is fundamental to our democracy," House Minority Leader Nancy Pelosi said in a statement. "At best, President Trump has committed a grave abuse of executive power. At worst, he has obstructed justice."
Senate Minority Leader Chuck Schumer, discussing the latest developments on the the Senate floor, said: "The country is being tested in unprecedented ways. I say to all of my colleagues in the Senate, history is watching."