However, this was the "one last chance to comply" for the Federal Bureau of Investigation and the Justice Department, he said.
Even if impeachment were to pass Congress, a two-thirds majority in the Senate would be needed to convict Rosenstein and remove him from office.
"For nine months we've warned them consequences were coming, and for nine months we've heard the same excuses backed up by the same unacceptable conduct", Meadows, chairman of the staunchly conservative Freedom Caucus, said in a statement Wednesday night.
"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". Attorney General Jeff Sessions put a USA attorney, John Lausch, in charge of providing Congress with the documents.
Democrats have criticized Republican efforts to pressure the Justice Department in recent months, saying they are attempts to undermine Mueller's investigation. "The president has been clear that he wants the DOJ to be transparent and cooperate with Congress", spokesman Hogan Gidley told reporters.
In what progressive advocacy groups and House Democrats immediately decried as a "shameless political ploy" aimed at shielding President Donald Trump from Special Counsel Robert Mueller's ongoing Russian Federation probe, Reps.
The resolution was filed by Republican Reps.
Rosenstein says that's not true.
Rosenstein was appointed to investigate alleged ties between the Trump campaign and Russia
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.
Republicans in the House have been discussing possible impeachment action against Rosenstein for some time.
The impeachment resolution came about two hours after GOP lawmakers met with Justice Department officials about the documents.
On "America's Newsroom", Dershowitz, a Harvard Law professor emeritus, reiterated what he wrote in his book, "The Case Against Impeaching Trump".
Asked in May about rumblings that House Republicans might move to impeachment, Rosenstein was defiant.
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.
Meadows accused Rosenstein of "stonewalling" Congressional oversight.
At a weekly news conference, Mr Ryan - who is stepping down at the end of his term - said Mr Rosenstein's actions do not rise to a level that would warrant impeachment under the United States constitution.
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