Rep. Mark Green Mark GreenOn The Money: House panel pulls Powell into partisan battles | New York considers hiking taxes on the rich | Treasury: Trump's payroll tax deferral won't hurt Social Security House panel pulls Powell into partisan battles over pandemic GOP lawmakers want answers from Disney on Mulan, China MORE (R-Tenn.) introduced a resolution to force a House vote this week on whether to refer Michael Cohen Michael Dean CohenJudge orders Eric Trump to comply with New York AG's subpoena before Election Day A huge deal for campaign disclosure: Trump's tax records for Biden's medical records Our Constitution is under attack by Attorney General William Barr MORE's recent congressional testimony to the Justice Department for a perjury investigation.

Green introduced a privileged resolution Tuesday afternoon to give the Democratic-controlled House 48 hours to vote on the resolution he introduced earlier this month.

A vote related to the resolution is expected to occur on Wednesday, according to the office of House Majority Leader Steny Hoyer Steny Hamilton HoyerOVERNIGHT ENERGY: California seeks to sell only electric cars by 2035 | EPA threatens to close New York City office after Trump threats to 'anarchist' cities | House energy package sparks criticism from left and right House energy package sparks criticism from left and right Hoyer: House should vote on COVID-19 aid — with or without a bipartisan deal MORE (D-Md.).

Green's spokesman Mitchell Hailstone told The Hill added that Green and other Republican lawmakers believe that Cohen lied under oath six times while testifying before the House Oversight and Reform Committee in February.

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A representative for Cohen did not immediately respond to The Hill's request for comment.

Green, who is on the Oversight and Reform Committee, introduced the resolution to refer the testimony to the Justice Department earlier this month.

"If Chairman [Elijah] Cummings fails to refer Mr. Cohen to the Department of Justice for perjury, it will forever mar the reputation of the Oversight committee and call into question the integrity of the entire House," he said in a statement at the time.

"Mr. Chairman, do what you said you'd do and hold Mr. Cohen accountable for lying before our committee," he added.

Cohen was previously sentenced to three years in prison for lying to Congress. He was President Trump Donald John TrumpBiden on Trump's refusal to commit to peaceful transfer of power: 'What country are we in?' Romney: 'Unthinkable and unacceptable' to not commit to peaceful transition of power Two Louisville police officers shot amid Breonna Taylor grand jury protests MORE's personal attorney before the relationship went bad and he began cooperating with prosecutors with the Southern District of New York.

The House Intelligence Committee will be referring a different ally of the president, Erik Prince, to the department on accusations of lying to Congress, Chairman Adam Schiff Adam Bennett SchiffPelosi, Democrats unveil bills to rein in alleged White House abuses of power Chris Matthews ripped for complimenting Trump's 'true presidential behavior' on Ginsburg Trump casts doubt on Ginsburg statement, wonders if it was written by Schiff, Pelosi or Schumer MORE (D-Calif.) said Tuesday.

—Updated at 2:23 p.m.