Rosenstein's interview comes after he canceled one with lawmakers last week, after meeting with President Trump.
"I committed I would ensure the investigation was appropriate and independent and reached the right result, whatever it may be", Rosenstein said. "And if I were Congress, I'd be having Mr. Mueller come in and testify". Meadows wrote on Twitter that Rosenstein "has not cooperated with Congress, failed to be transparent about his actions, and shown a lack of candor in the way he's characterized a number of events". He didn't answer questions about the Times story.
Rosenstein was also a signer of the FBI's suspect application to the Foreign Intelligence Surveillance Act (FISA) court for approval of government spying on former Trump campaign aides.
Special Counsel Robert Mueller is expected to present his findings on the two core issues of the Trump-Russia probe, collusion and obstruction, "soon after the November midterm elections".
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James Milner also trained on Thursday, having injured his hamstring in Liverpool's game with Manchester City over the worldwide break.
The interview will be conducted by House Judiciary Committee Chairmen Bob Goodlatte (R-VA) and Trey Gowdy (R-SC) along with Ranking Members Jerry Nadler (D-NY) and Elijah Cummings (D-MD). He's among the Republicans who have accused the agencies of bias against the president.
Trump and Rosenstein have had an up-and-down relationship, though the deputy has been spared the brunt of the anger directed at his boss, Attorney General Jeff Sessions. And Rosenstein has wide discretion on what he releases to Congress, and whether he releases any of it publicly.
There was speculation weeks ago that Rosenstein would be fired or resign following a New York Times report that he had discussed secretly recording Trump previous year. Rosenstein has denied the reports are accurate. But the story was subsequently updated to say it was not clear what the reaction was to the offer.