House Republicans are demanding that a transcript of former Trump personal attorney Michael Cohen Michael Dean CohenA huge deal for campaign disclosure: Trump's tax records for Biden's medical records Our Constitution is under attack by Attorney General William Barr Eric Trump says he will comply with New York AG's subpoena only after Election Day MORE's testimony before lawmakers be sent to the Department of Justice (DOJ) for a potential perjury investigation.

Rep. Mark Green Mark GreenGOP lawmakers want answers from Disney on Mulan, China House GOP Steering Committee selects four members for new committee positions Hillicon Valley: DOJ indicts Chinese hackers accused of targeting COVID-19 research | House votes to ban TikTok on government devices MORE (R-Tenn.) introduced the privileged resolution on Wednesday. It directs Oversight and Reform Committee Chairman Elijah Cummings Elijah Eugene CummingsBlack GOP candidate accuses Behar of wearing black face in heated interview Overnight Health Care: US won't join global coronavirus vaccine initiative | Federal panel lays out initial priorities for COVID-19 vaccine distribution | NIH panel: 'Insufficient data' to show treatment touted by Trump works House Oversight Democrats to subpoena AbbVie in drug pricing probe MORE (D-Md.) to send a copy of the Cohen transcript to the DOJ for review.

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Supporters of the measure argue Cummings failed to live up to his promise to hold Cohen accountable after they accused him of lying under oath, arguing the former lawyer to President Trump Donald John TrumpOmar fires back at Trump over rally remarks: 'This is my country' Pelosi: Trump hurrying to fill SCOTUS seat so he can repeal ObamaCare Trump mocks Biden appearance, mask use ahead of first debate MORE misled the panel at least seven times while testifying in February.

“We're making a simple request today that Democrats protect the integrity of the House of Representatives and refer Michael Cohen to the Department of Justice for perjury. Why is this controversial?” Green, who was joined by a group of House Oversight Republicans, told reporters at a press conference.

“Michael Cohen swore under oath to tell the truth before the House Oversight Committee, but he lied and multiple times. Ranking Member [Jim] Jordan [R-Ohio] and the rest of us warned the Democrats that we couldn't trust a man who was going to jail for lying to Congress — that's just common sense," he said.

Jordan, the top Republican on the Oversight panel, told reporters he doesn’t believe there is any disagreement between parties over whether Cohen lied to Congress, adding, “I just think they're not willing to do what they said they were going to do.”

Cohen, who was the first witness called before the committee after Democrats took control of the panel this year, repeatedly told lawmakers that he “never” asked for a pardon before backtracking on his remarks.

House Majority Leader Kevin McCarthy Kevin Owen McCarthyMcCarthy's Democratic challenger to launch first TV ad highlighting Air Force service as single mother Trump asked Chamber of Commerce to reconsider Democratic endorsements: report The Hill's Morning Report - Sponsored by The Air Line Pilots Association - White House moves closer to Pelosi on virus relief bill MORE (R-Calif.) blasted Democrats on the committee for failing to act swiftly to refer Cohen to the DOJ, adding they should have been wary of bringing a witness in who was slated to go to prison for lying under oath.

“If you [Cummings] were not willing to stand up to someone who lied before your committee, you should not have told the American public that,” he said.

“Jim Jordan James (Jim) Daniel JordanSunday shows preview: Justice Ginsburg dies, sparking partisan battle over vacancy before election House passes resolution condemning anti-Asian discrimination relating to coronavirus Republicans call for Judiciary hearing into unrest in cities run by Democrats MORE has been patient, Jim Jordan has worked with this chairman. Forty-two days is patient enough,” McCarthy said.

Rep. Mark Meadows Mark Randall MeadowsHouse moves toward spending vote after bipartisan talks House Democrats mull delay on spending bill vote Southwest Airlines, unions call for six-month extension of government aid MORE (R-N.C.), the chairman of the conservative House Freedom Caucus, said it’s critical to get members on the record on the issue. He argued lawmakers need to hold witnesses accountable to uphold the integrity of the panel.

"Hopefully, we will see the Democrats have come together in a bipartisan way to say that we will not allow a witness to come in here and lie and lie and admit, even by his own attorney's admission, that perhaps the testimony he gave was not exactly the truth,” he said.

“And and so we have this particular resolution that in two weeks will be having a vote on. And it will be up to Speaker [Nancy] Pelosi [D-Calif.] to decide on whether that's going to be a bipartisan vote, standing up for this institution, or whether it will be exercised in a privileged manner to make sure that everyone goes on record,” Meadows said.

Cohen is scheduled to report to prison on May 6 after pleading guilty last year to a series of crimes while working for Trump. He was sentenced in December to 36 months in jail and used his congressional testimony earlier this year to further implicate Trump in a hush money scheme before the 2016 election.