(CNN) House Speaker Paul Ryan said Thursday he does not support House conservatives' efforts to impeach Deputy Attorney General Rod Rosenstein as the House Freedom Caucus leaders backed down -- for now.

Ryan's comments opposing the impeachment of Rosenstein, who supervises special counsel Robert Mueller's investigation, came as Freedom Caucus leader Mark Meadows, a North Carolina Republican, said an agreement was reached to give the Justice Department and the FBI "one more chance" to turn over documents to Congress, but has not specified what materials have been improperly withheld.

Ryan made clear at his weekly news conference that he thought impeachment was a step too far.

"I don't think we should be cavalier with this process or with this term," the Wisconsin Republican said. "I don't think that this rises to the level of high crimes and misdemeanors. (It's) a really high standard. ... Since I got involved, (we) have been getting a lot of compliance from (the Justice Department) on the document request. We do not have full compliance, and we have to get full compliance, but we've been making tremendous progress to that point."

On Wednesday evening, Meadows and Ohio Republican Rep. Jim Jordan -- who announced a bid for speaker Thursday -- introduced a resolution to impeach Rosenstein, but they didn't use a "privileged" House procedure to force a vote on the matter.

The push came as the House left town Thursday to kick off a month-long recess until September.

Meadows downplayed any disagreement with the speaker on the matter, saying he had spoken to the speaker on Thursday morning. And on the House floor during votes, House Majority Whip Steve Scalise of Louisiana and Judiciary Chairman Bob Goodlatte of Virginia spoke with Meadows and other House Freedom Caucus members, where an apparent agreement was struck.

"All of that came to an agreement where we felt like not doing a privileged motion today would be most prudent ... and yet brings us all together the first week in September if they do not comply," Meadows said. "The speaker is willing to support Chairman Goodlatte in a contempt process if the agreed upon documents are not delivered."

A contempt vote would still be a significant step against Rosenstein, but it's not as severe as trying to impeach him, which could result in a trial in the Senate if the vote was successful.

Meadows said that impeachment still remained on the table, noting that he could still bring a privileged impeachment resolution to the floor in September to force a vote on it.

Democrats charge that the effort to impeach Rosenstein is really an attempt to undercut Mueller's probe.

"The attack on Rosenstein of course is an attack on the Mueller investigation," House Minority Leader Nancy Pelosi, a California Democrat, said Thursday. "Hopefully saner minds will prevail on the Republican side and they won't bring this up."

GOP document demands

Meadows said Republicans planned to provide the Justice Department with a concrete list of documents to the Justice Department that it still had to turn over.

The subpoena issued by Goodlatte earlier this year covered a host of documents related to the FBI's handling of the Hillary Clinton email investigation and the probe into Donald Trump's campaign team and Russia.

Justice Department officials say they've turned over roughly 880,000 pages of documents related to the 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. Other documents requested in the subpoena were so sensitive that the FBI had to build a new search tool to gather the materials lawmakers requested, officials explained Wednesday, which accounted for some of the delays.

Oversight Chairman Trey Gowdy, who says he's opposed to trying to impeach Rosenstein, said that DOJ has "provided a lot of documents," but it's still not full compliance.

"I've never been that interested in the total documents produced, unless I know the total number of documents that would be relevant," said Gowdy, a South Carolina Republican.

Meadows told reporters "we were able to make some other concessions and agreements," but the Justice Department hasn't "conceded" anything on document production, according to a source familiar with the discussions. In fact, as of early Thursday afternoon, there had been no discussions between Meadows and the department since he filed his resolution following the Wednesday afternoon meeting between lawmakers DOJ officials, the source said.

Justice officials say that the only document being withheld is the "scoping" memo written by Rosenstein that outlines scope of Mueller's authority. All of the other documents have either been produced or are in process of being redacted to be produced, according to Justice officials.

While the scoping memo is cited in Meadows' impeachment resolution, he acknowledged Thursday that it fell outside the subpoena and might not need to be produced in order for the Justice Department to comply with the subpoena.

"If the March 22 subpoena is complied with and the scope memo is not provided, then I think most of us would view that they are in compliance with a valid subpoena," Meadows said.

Reservations about impeachment

The impeachment resolution that Meadows introduced cited a litany of complaints against Rosenstein. In addition to stonewalling the GOP subpoenas, the impeachment resolution faulted Rosenstein for signing one of the Foreign Intelligence Surveillance Act warrant renewals on Carter Page , and refusing to turn over scoping memo.

But it's not clear that Meadows would have the votes for impeachment, and he acknowledged Thursday that the resolution likely would fail in the House if a vote was held Thursday.

In addition to Ryan's concern, Gowdy reiterated his opposition to impeachment Thursday, saying he didn't want the "drama," only the documents.

Several other rank-and-file Republicans also expressed their own reservations.

Rep. Tom Rooney, a retiring Florida Republican on the Intelligence Committee -- which has had its own major document fight with the Justice Department -- says he has an open mind about impeachment but is inclined to oppose it at this point.

"When I see how they're laying it out or what they're saying then I'll make up my mind," Rooney said. "From what I know now my predisposition is not to support that."

"I'm as troubled as anyone by this," Rep. Chris Stewart, a Utah Republican, said of the difficulty obtaining documents. "I think if we're going to impeach though we have to have a process. I think we should have hearings and we should have a debate on the floor. I think we should convince the American people it's the right thing to do. I'm not sure we've done that yet."

And Rep. Ileana Ros-Lehtinen, another Florida Republican retiring at the end of the term, said she was opposed to impeaching Rosenstein and thought the broader Republican conference was too.

"I think that they are maneuvers that certain Republicans are trying to end the Mueller investigation, and they're taking pot shots at it along the way," she said. "I hope that we do have the vote so we can vote it down."

This story has been updated with additional developments Thursday.