The head of the House Oversight and Reform Committee on Wednesday rejected the request of two GOP committee members to join them in making a criminal referral of 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 to the Justice Department for possible perjury charges over his testimony.

Cohen, 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's former personal attorney, told the Oversight and Reform Committee in sworn testimony last month that he had never solicited a pardon from the president, though his own lawyer has since sought to clarify those comments.

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“Our practice on this Committee is to give witnesses an opportunity to clarify their testimony, and that is what Mr. Cohen has done. I do not see the need for further action — at least at this time," 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.) said in a statement on Wednesday.

Cummings, however, noted that he will review the transcript of Cohen's closed-door testimony with the House Intelligence Committee, and lawmakers on the panel can then "determine whether any additional steps are required.”

His response came 20 minutes after Reps. 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 (R-Ohio), the ranking member on the Oversight panel, and 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.) asked Cummings in a letter to join them in their referral, stating that the president's former personal lawyer was "unequivocal" when he denied he would seek a pardon.

"In light of mounting evidence, it appears Cohen likely lied under oath during his appearance before the Committee," they write, alleging that his sworn testimony "appears on its face to be demonstrably false."

"Cohen's denial of ever seeking a pardon, which he made during his carefully crafted opening statement, contained no qualifiers about the context of his statement. ... In fact, there is no mention whatsoever in Cohen's prepared testimony about the joint defense agreement. Simply put, Cohen's denial of ever seeking a pardon, as uttered under oath in his testimony, was absolute and unequivocal," they continue.

"I don’t know if he lied or not," Hill said. "Chairman Cummings is incredibly deliberate. I know that he's reviewing the entire testimony, all the transcripts with [Jordan], who also is going to make sure that we get to the bottom of this," Hill said on "Fox News Sunday."

The back-and-forth letters come one day after Michael Monico, an attorney for Cohen, sent a letter to Cummings seeking to clarify his testimony.

“In retrospect, while the sentence could have been clearer regarding the time frames, the sentence is true, and Mr. Cohen stands by his statement,” the letter reads.

Monico, however, maintained that his client was telling the panel the truth when Cohen said he had not sought a pardon, because he was referring to the time since a joint-defense agreement with the president ended last June.

While Cohen had told his lawyers to explore the possibility of a pardon when it was offered by the president's legal representatives following last year's FBI raids on his home and office, he did has not asked for a pardon since his joint-defense agreement ended, Monico said.