Representatives Jim Jordan and Mark Meadows, who belong to the conservative House Freedom Caucus, joined nine other House members in accusing Rosenstein of hiding investigative information from Congress, failure to comply with congressional subpoenas and other alleged misconduct.
Their move came two hours after GOP lawmakers met with Justice Department officials who have been working to provide documents to several congressional committees about decisions made during the 2016 presidential campaign.
"The DOJ has continued to hide information from Congress and repeatedly obstructed oversight-even defying multiple Congressional subpoenas", Meadows wrote on Twitter. One Republican, House Oversight and Government Reform Committee Chairman Trey Gowdy (R-S.C.), said he thinks the department is coming around on document requests.
"The DOJ is keeping information from Congress", Jordan said, referring to the Department of Justice.
A House GOP aide told ABC News Wednesday night that the articles of impeachment were not filed as a "privileged resolution," meaning they can not force a vote on it on the House floor.
Rosenstein oversees special counsel Robert Mueller's investigation of Russian election meddling and possible ties to the Trump campaign.
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.
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'It's time to find a new deputy attorney general who is serious about accountability and transparency, ' he added.
Rosenstein is accused violating Congressional subpoenas by withholding requested documents pertaining to Mueller's ongoing investigation and for allegedly abusing the Foreign Intelligence Surveillance Act, through which warrants against Trump campaign aide Carter Page were issued past year.
It's unclear if there will be an immediate vote.
"Deputy Attorney General Rosenstein's failure to recuse himself in light of this inherent conflict of interest and failure to recommend the appointment of a second special counsel constitute dereliction of duty".
House Intelligence Committee ranking member Rep. Adam Schiff (D-Calif.) also decried the motion in a tweet.
House Speaker Paul Ryan has also said he is satisfied with progress on the document production.
Democrats have argued the focus on Rosenstein is an attempt to broadly undermine the Mueller investigation.
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.