Mark Meadow, Jim Jordan, and nine others from the so-called Freedom Caucus-all strong allies of President Donald Trump.
Justice Department officials said they have provided the vast majority of information sought in subpoenas from two key House committees - and are almost done with providing all of the outstanding information requested in those subpoenas.
"With Attorney General Sessions' recusal, Rod Rosenstein has been in charge of the Department of Justice as the agency has made every effort to obstruct legitimate attempts of congressional oversight", Meadows said. "It's time to find a new Deputy Attorney General who is serious about accountability and transparency", Meadows said in a statement.
Minutes later, House Republicans voted to sanction the Department of Justice over GOP document requests.
"We've caught the Department of Justice hiding information, redacting information that they should not have redacted", Jordan charged, adding that Rosenstein had attempted to intimidate House staffers with subpoenas.
Most recently, lawmakers have focused on what they call Rosenstein's failure to hand over documents or disclose other information as the main reason he must be removed.
Democrats have accused Republicans of trying to discredit the Justice Department, and, by extension, the special counsel's probe into Russian interference in the 2016 US election.
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House Republicans somehow located their oversight powers for Rod Rosenstein, but for the rest of the executive branch (Trump) it's all sad tweets and reporter runarounds.
The Justice Department declined to comment.
Rosenstein, the No. 2 official at the Justice Department, has become a frequent punching bag for supporters of President Donald Trump for appointing Mueller to investigate whether Trump's campaign colluded with Russian Federation in his race against Democrat Hillary Clinton. But with House Speaker Paul Ryan among those opposed, the resolution is unlikely to go as far as a vote.
If the proposal cleared the House, it would need a two-thirds vote in the Senate for Rosenstein to lose his job. Sen.
"The DOJ is keeping information from Congress", Jordan said, referring to the Department of Justice.
Republican leaders, however, have said in recent weeks that they are satisfied with the Justice Department's progress.
"This is part of a sustained, coordinated effort to undermine the investigation of Robert Mueller and the work of the FBI and the Department of Justice, to attack the credibility of the investigators", Rep. David Cicilline, D-R.I., a member of the Judiciary Committee, told ABC News last month. They say that Rosenstein has a conflict of interest by having both been involved in that application and overseeing Mueller's efforts.