By Jeremy Herb and Laura Jarrett, CNN

(CNN) -- Deputy Attorney General Rod Rosenstein has agreed to speak with House Republicans about his reported comments discussing wearing a wire to talk to President Donald Trump and recruiting Cabinet members to invoke the 25th Amendment to remove him from office, according to sources familiar with the matter.

House Republican leaders struck an agreement with House Freedom Caucus leaders for Rosenstein to appear to explain his comments, staving off a potential bid to try to force an impeachment vote against the deputy attorney general.

The details of the sit-down remain unclear, however, as Judiciary Chairman Bob Goodlatte, a Virginia Republican, and the leaders of the House Freedom Caucus who demanded Rosenstein's appearance described it in different terms Friday.

In a statement, Goodlatte said Rosenstein had been invited "to come in for a private meeting in the coming weeks."

But the Freedom Caucus leaders, Reps. Mark Meadows of North Carolina and Jim Jordan of Ohio, said they believed Rosenstein would be coming for a transcribed interview as part of the congressional investigation into the FBI's handling of the Hillary Clinton and Russia investigations.

"I thought it was a transcribed interview with both Republicans and Democrats there. I thought it would be the same format we've used before," Jordan said.

"Leadership has agreed to call Rod Rosenstein before Congress, for a closed-door hearing with our panel investigating, so he can explain his alleged comments on 'wiring' POTUS--as well as other inconsistent statements," Meadows tweeted Friday morning. "If Mr. Rosenstein fails to show up, we will subpoena him."

Politico first reported the plan to call Rosenstein in for a closed meeting.

Goodlatte invited Rosenstein to come to Capitol Hill after Meadows had threatened earlier in the week to force an impeachment vote against Rosenstein if he did not testify. House Republican leaders met with Meadows and Jordan on Wednesday and Meadows agreed not to move forward with impeachment at this point.

A DOJ official said that Rosenstein and Goodlatte spoke Thursday evening and agreed to meet in the next few weeks.

Democrats raised concerns that a private meeting would mean they were not included in the conversation with Rosenstein. "There is no such thing as a 'closed, private hearing,'" Rep. Jerry Nadler, the top Democrat on the House Judiciary Committee, tweeted Friday morning. "The @HouseGOP cannot be left alone in a room with DAG Rosenstein."

But House Oversight Chairman Trey Gowdy, whose committee has worked with Goodlatte's on the FBI investigation, said that Democrats were "encouraged to attend," though it would not be a full committee meeting with Rosenstein.

Jordan and Meadows said they expected Rosenstein would come to Capitol Hill within the next two weeks, though a date was not finalized.

On Monday, Rosenstein momentarily appeared to be on his way out of the Justice Department, but now he appears to be staying put for the time being, as Trump delayed a planned meeting with his deputy attorney general on Thursday.

But Rosenstein, who supervises special counsel Robert Mueller's probe, has long been in the crosshairs of Trump's Republican allies in Congress who have fought with the Justice Department for months over documents related to the FBI's Clinton and Trump-Russia investigations.

Reports from The New York Times, CNN and others that Rosenstein had discussed a wire and the 25th Amendment added fuel to the Rosenstein criticisms, although Trump's allies in Congress stopped short of calling for Rosenstein's firing. Rosenstein said he never pursued recording the President and denied any suggestion he advocated for Trump's removal, and one source in the room for the wiretapping comment dismissed it as sarcasm.

Goodlatte did not subpoena Rosenstein for his testimony this week as Meadows and Jordan had demanded, but he did issue a subpoena for the memos from former FBI Deputy Director Andrew McCabe that documented Rosenstein's comments.

Ryan said Wednesday that the President should work out the issue with Rosenstein and Congress shouldn't "step in the way of that."