They also grilled him on the timeline of his controversial memo that Trump used as a rationale for sacking FBI director James Comey last week, with two senators saying Rosenstein acknowledged he knew before writing his brief that the president was going to fire Comey.
"He knew the day before" the May 9 firing, Senate Democrat Dick Durbin told reporters as he exited the secure briefing in the basement of the Capitol, where all 100 senators had been invited to attend.
"On May 8th he learned that the president was going to terminate Comey," Durbin added. Democrat Claire McCaskill corroborated Rosenstein's remarks.
A third senator, Republican Bill Cassidy, said Rosenstein "indicated what Donald Trump has indicated, that Mr. Trump was leaning in that direction" before Rosenstein presented his memo.
Rosenstein and Attorney General Jeff Sessions met with Trump May 8, when the president asked them to put into writing their thoughts on Comey.
Initially it was Rosenstein's memo -- critical of Comey's handling of the Hillary Clinton email scandal last year -- that was put forward as the justification for the dismissal.
Then Trump admitted he had been considering firing Comey for months.
Republican Senator Marco Rubio said he has "full confidence" in Mueller. "He's going to conduct a fair and thorough investigation, of that I have no doubt."
A number of lawmakers exited the meeting stressing that Mueller's probe, while appropriately diving in to all possible Trump-Russia ties, may make it more difficult for current congressional investigations to access vital intelligence.
"I think we'll have a more difficult time getting information here for the intelligence committee," Republican Senator Ron Johnson said.
The Senate Intelligence Committee and House Government Oversight Committee have each requested Comey testify before their panels.
(This story has not been edited by NDTV staff and is auto-generated from a syndicated feed.)
Get Breaking news, live coverage, and Latest News from India and around the world on NDTV.com. Catch all the Live TV action on NDTV 24x7 and NDTV India. Like us on Facebook or follow us on Twitter and Instagram for latest news and live news updates.