(CNN) The full House of Representatives is expected to vote on June 11 to hold Attorney General William Barr and former White House counsel Don McGahn in contempt of Congress, even as House Speaker Nancy Pelosi continues to reject calls to go further and impeach President Donald Trump.

In a private leadership meeting Monday evening, Pelosi discussed her party's next steps for Barr with the contempt vote. According to four sources, Pelosi also made clear her opposition to opening up impeachment proceedings. One source in the room said she was critical of those pushing impeachment, like billionaire Democratic donor Tom Steyer, because she said they seem to believe impeachment will remove Trump, ignoring the role of the GOP-controlled Senate.

Shortly thereafter, House Majority Leader Steny Hoyer -- the second ranking Democrat in the chamber -- announced in a statement the plans to vote on holding Barr and McGahn in contempt.

"Next Tuesday, I will bring a resolution to the House Floor forcing Attorney General Barr and former White House Counsel McGahn to comply with Congressional subpoenas that have been duly issued by the House Judiciary Committee," Hoyer said in the statement.

He added later, "This Administration's systematic refusal to provide Congress with answers and cooperate with Congressional subpoenas is the biggest cover-up in American history, and Congress has a responsibility to provide oversight on behalf of the American people."

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