(CNN) President Donald Trump's Republican congressional allies are calling on Deputy Attorney General Rod Rosenstein to testify before Congress about reports he discussed wearing a wire to record the President and invoking the 25th Amendment to remove Trump from office.

The Republicans say they want Rosenstein to testify under oath this week about what he said, and one suggested they might force a House vote on impeaching Rosenstein if he doesn't appear.

The Republican demands come ahead of a scheduled Thursday meeting between Trump and Rosenstein to decide the fate of the deputy attorney general, who supervises special counsel Robert Mueller's investigation.

The denials didn't satisfy the congressional Republicans who have been staunch critics of Rosenstein. They seized on the report to call for Rosenstein's testimony as well as for the Justice Department to provide Congress with memos from former Deputy FBI Director Andrew McCabe that documented the conversations in question.

"You can't have the number two official at the Department of Justice making comments about wiring the President and not address it," House Freedom Caucus leader Mark Meadows tweeted. "Rod Rosenstein must come before Congress this week, under oath, and tell the truth about his alleged statements."

Rep. Matt Gaetz, a Florida Republican, told CNN's Chris Cuomo that he and Meadows were considering an impeachment vote on Rosenstein. Under House rules, they would be able to force a procedural vote on articles of impeachment.

"I don't think it's appropriate to joke about taking an action against the institution of the presidency while you're overseeing an investigation," Gaetz said, telling Cuomo it was "probably" a fireable offense even if it was a joke.

"Rod Rosenstein's impeachment can be brought up for a vote by any member of Congress at this point. It lights a two-day fuse," Gaetz added. "If we don't get these answers under oath, we may invoke that vote to keep the Congress in town so we can get to the bottom of this."

And Rep. Jim Jordan, an Ohio Republican who got into a heated exchange with Rosenstein when he testified in June , said that even if Rosenstein was joking, it wouldn't excuse the comment.

"He should be in front of the House Judiciary Committee as soon as possible to answer our questions," Jordan said in a Fox Business Network interview. "You cannot have the top guy in the Justice Department, which is what Mr. Rosenstein is in effect, talking to subordinates about recording the commander in chief, even if it was done in a sarcastic way. You cannot have that happen."

House Judiciary Chairman Bob Goodlatte, a Virginia Republican, threatened to subpoena for McCabe's memos in an interview on Fox News' "Sunday Morning Futures," but he has not weighed in about Rosenstein testifying this week. A Goodlatte spokeswoman declined to comment.

Democrats have had a starkly different reaction to the prospect that Rosenstein could be fired or resign, warning that Rosenstein's ouster is a threat to the Mueller probe.

"The last thing our nation needs is a slow motion Saturday Night Massacre, by which the President engineers the firing of Justice Department officials charged with supervising the special counsel investigation," New York Rep. Jerry Nadler, the top Democrat on the Judiciary Committee, said in a statement.

Nadler and other Democratic lawmakers have called for Congress to pass legislation to protect the special counsel investigation, a bill that Republican leaders have said is unnecessary.

Rosenstein has long been under fire from congressional Republicans, who have accused him and the Justice Department of stonewalling their efforts to obtain documents related to the department's handling of the Hillary Clinton email and Trump-Russia investigations. Meadows and Jordan introduced articles of impeachment against Rosenstein in July, though House GOP leadership has thus far persuaded them forcing a floor vote on the matter.

Rosenstein has pushed back against his congressional critics, including the last time he testified before the House Judiciary Committee in June.