The South Carolina Republican said he wasn't able to ask specifically if it was now a criminal probe "but the takeaway have is everything he said was that you need to treat this investigation as if it may a criminal investigation".
Rosenstein briefed the US Senate just one day after he turned the political world on its head by appointing a special counsel to investigate possible collusion between the campaign of President Donald Trump and Russian officials meddling in last year's election.
Graham said he thinks "Congress' ability to conduct investigations of all things Russia has been severely limited, probably in an appropriate fashion."
That would make it harder to subpoena records of people who could be subjects of the investigation, he added.
Rosenstein was originally invited by the two Senate leaders, Republican Mitch McConnell of Kentucky and Democrat Chuck Schumer of New York, to explain Trump's firing of FBI Director James Comey. But that changed on Wednesday evening when Rosenstein announced that he had appointed another former FBI director, Robert Mueller, to conduct an independent investigation into Russia's interference in the 2016 campaign.
Sen. Marco Rubio, a Florida Republican, said senators asked about 35 questions and described the meeting as "enlightening but not overly informative."
A House Republican aide said Wednesday that House Speaker Paul Ryan of Wisconsin invited Rosenstein to brief all House members on the investigation Friday morning.
Rosenstein's announcement followed more than a week of chaos emanating from the White House, starting with Comey's firing last Tuesday and continuing through the news Monday that Trump divulged classified information to Russian officials and Tuesday's stunning report that Trump asked Comey in a private meeting to stop his investigation into former national security adviser Michael Flynn.
By Wednesday, leaders from the Senate intelligence and judiciary committees had sent requests to both the FBI and the White House for all records pertaining to Comey's conversations with Trump. And House and Senate investigators had invited Comey back to Congress to explain what happened -- although Utah Rep. Jason Chaffetz declared on Twitter
that he had trouble finding Comey to invite him to testify to the oversight committee he chairs.
Meanwhile, Senate Democrats met in private Wednesday to brainstorm how they were going to grill Rosenstein -- including pressing him to name a special prosecutor. A few hours after their meeting, the question became a moot point.
By Wednesday evening, a Republican source said that the move effectively shut down Congress' intense digging into Comey and his conversations with Trump.
"This shuts the whole thing down," said one Republican source, speaking on Congressional efforts to investigate Comey's discussions with Trump.
The focus now turns to how Mueller will pick up the FBI's investigation of the Trump campaign and Russia, and what it means for the White House.
"If your implication is that the White House wants this, I think that's wrong," said Senate judiciary chair Chuck Grassley Wednesday night. Rosenstein's "got the power to do it and you have to accept it and it doesn't matter what we think. It's a fait accompli."
Asked if Mueller's appointment would preempt his own request for Comey information, the Iowa Republican replied, "I don't know."