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(CNN) —  

House Freedom Caucus leaders Reps. Mark Meadows and Jim Jordan on Wednesday escalated their fight with the Justice Department, introducing a resolution to impeach Deputy Attorney General Rod Rosenstein.

The resolution is not a sign that the House is about to vote to impeach Rosenstein, as House Judiciary Chairman Bob Goodlatte and House Oversight Chairman Trey Gowdy – who have been pushing for documents from the Justice Department – did not sign on. The House is also leaving for a monthlong recess after Thursday.

The resolution to impeach Rosenstein, which Meadows and his conservative allies have been threatening for weeks, is the strongest step that conservative allies of President Donald Trump have taken in their feud with Rosenstein and the Justice Department.

In a statement, Meadows said Rosenstein should be impeached because of the Justice Department’s stonewalling of congressional subpoenas and hiding information from Congress, and for signing one of the Foreign Intelligence Surveillance Act warrant renewals for Trump campaign foreign policy adviser Carter Page.

Rosenstein has fiercely pushed back against his House Republican critics, warning in May that the Justice Department is “not going to be extorted” amid threats that he could be impeached.

The impeachment resolution that Meadows introduced was not “privileged,” which is a procedural motion that can force a House floor vote on the matter, a move that liberal Democrats have already taken against the President, though it was easily voted down.

A Meadows spokesman said the North Carolina Republican was leaving open the option of making the resolution privileged to force a vote. But such a move isn’t likely to occur until after the House returns in September.

“Information has been hidden, efforts have been stonewalled,” Meadows said during an appearance on Fox News Wednesday night. “I guess for us, it’s all about transparency so the American people can judge for themselves. They may be able to ignore Congress but they can’t ignore the American people.”

Later in the Fox News interview, Meadows hinted he may try to force a vote on the House floor about the articles of impeachment against Rosenstein as soon as Thursday. Meadows said he doesn’t want to bring the motion to the floor without Ryan’s permission but that it’s possible it can happen.

“But starting tomorrow, we can bring it up as a privileged motion,” he said.

He added, “It really means it would require a vote on the House floor within two days and that’s something that any member of Congress, Jim or I, can do. And quite frankly, it’s either we hold him in contempt or we get the documents or we impeach him, and the only thing we have control over is the ability to bring impeachment straight to the floor.”

Rosenstein has been in the crosshairs of conservative Republicans – as well as Trump – for a number of reasons, including his role supervising special counsel Robert Mueller’s investigation into Russian interference in the 2016 US election.

He has been faulted, in part, because of an accusation that the original FISA application on Page was based on “political opposition research (that) was neither vetted before it was used in October 2016 nor fully revealed” to the FISA court, according to the articles of impeachment. Yet Rosenstein was not sworn in as the No. 2 official at the Justice Department until six months later, in April 2017. He did sign off on at least one request to renew FISA warrant after taking office.

Democrats charge that Republicans are targeting Rosenstein because they’re trying to undercut Mueller’s probe.

The impeachment resolution was formally introduced after a meeting Wednesday between senior Justice Department officials and Goodlatte, Gowdy, Meadows and Jordan, which Rosenstein did not attend.

Leaving the meeting, Meadows said he still had “great frustration” that the Justice Department had not complied with congressional subpoenas, although he declined at that point to comment on the prospect of impeaching Rosenstein.

While Meadows then moved on the impeachment resolution, others had a more positive view of the meeting. Gowdy, who is opposed to trying to impeach Rosenstein, told reporters afterward that he thought the meeting had been productive “because we’re making progress towards compliance.”

“I want the documents and I’m not a big fan of drama, I like the documents,” the South Carolina Republican said, explaining that he opposes impeachment because it’s punishment and not a remedy to obtaining the documents in question.

The Justice Department declined to comment.

The fight over documents between Congress and the Justice Department boils down to subpoenas from the House Judiciary and Intelligence committees for documents related to the FBI’s Hillary Clinton email investigation and the probe into Trump’s team and Russia.

Justice Department officials maintain that lawmakers have been provided with nearly all the documents requested by the House Judiciary subpoena from March and that they have been trying to accommodate incoming requests from House Intelligence Chairman Devin Nunes.

The most substantial effort has surrounded roughly 880,000 pages of documents related to the Justice Department inspector general’s investigation into how the FBI handled the Clinton probe. Committee staff have been able to review the documents in a reading room at the Justice Department and then obtain copies of documents of interest – a laborious process being overseen by US Attorney John Lausch from Chicago.

In June, FBI Director Chris Wray testified that 100 FBI employees have been working around the clock to respond to lawmakers’ requests.

But Republican lawmakers maintain that while the Justice Department is turning over more materials, it has yet to fully comply with the subpoenas. The House passed a resolution last month demanding full compliance with the subpoenas.