Rep. Jim Jordan, R-Ohio, on Sunday stood by his efforts to impeach Deputy Attorney General Rod Rosenstein, despite criticism from top lawmakers including House Speaker Paul Ryan, R-Wis., and commentators like famed legal professor Alan Dershowitz.

“If they don’t give us the documents, if they don’t give us information that we as a separate and equal branch of government are entitled to have in order to get answers for the American people, then we will actually call the vote for the impeachment of Rod Rosenstein," Jordan said during an interview with John Catsimatidis on "The Cats Roundtable" that aired Sunday on New York radio station AM 970.

Jordan and his House Freedom Caucus colleague Rep. Mark Meadows, R-N.C., announced on Wednesday that they had filed a resolution with nine other members of Congress to impeach Rosenstein, claiming the Justice Department's No. 2 had hindered congressional oversight of special counsel Robert Mueller's federal Russia investigation.

[Related: GOP lawmakers file resolution to impeach Deputy AG Rod Rosenstein]

Ryan said he opposes impeaching Rosenstein, but Meadows has threatened to go around the speaker if the GOP leader won’t allow a floor vote on the resolution. However, any action on impeachment will have to wait as House lawmakers are on August recess.

A group of high-profile House Republicans have clashed with Justice Department and FBI officials in recent months as they pursue documents covering the Russia probe — including the FBI's use of informants to make contact with the 2016 Trump campaign and speculation it had abused Foreign Intelligence Surveillance Act powers to gather information on Trump associates — and its examination of Hillary Clinton's private email server.

Tensions culminated with House Intelligence Committee Chairman Devin Nunes, R-Calif., demanding the DOJ and the FBI provide the materials or be subject to "obstruction." The House then passed a resolution demanding the agencies hand over sensitive documents sought by Nunes, House Judiciary Committee Chairman Bob Goodlatte, R-Va., and House Oversight Committee Chairman Trey Gowdy, R-S.C.

Jordan, who on Thursday officially launched his bid to replace Ryan as House speaker, said that a Republican-controlled House under his leadership would make a more concerted effort to keep campaign promises made by GOP candidates in the lead-up to the 2018 midterm elections.

"President Trump is doing what he said," Jordan continued. "We need to do more of that in Congress, and that’s why I want to be speaker.”