"Mr. Mueller will tell us what we can get", Graham said, referring to former FBI Director Robert Mueller, who Rosenstein appointed as special counsel on Wednesday.
While President Donald Trump has called the probe "the single greatest witch hunt of a politician in American history!" The White House cited a letter from Rosenstein to the president advocating for Comey's dismissal over his handling of the investigation into Hillary Clinton's private email server.
At a press conference later on Thursday, Trump said, "I respect the move but the entire thing is a witch hunt". Lindsey Graham, South Carolina Republican, told reporters after the briefing.
Several members of Congress said that if Trump did suggest that Comey "let this go" regarding Flynn's Russian contacts, it was probably just a joke, light banter.
He added that although he's "not a legal authority", but that "the intelligence committee will get the facts".
Moments before Mr Trump weighed in on Twitter, Democratic Senator Joe Manchin welcomed the special counsel investigation and said it was important to get facts in the Russian Federation probe.
They've requested Comey hand over the memo he wrote which claims President Trump asked him to back off the investigation into National Security Adviser Michael Flynn.
"As a former FBI Director of 12 years with a strong track record of independence, Robert Mueller is fully equipped to perform a credible investigation", the Republican from Jonesboro said.More news: Skoda Karoq drip-feed continues with new close-up images
Rosenstein appointed ex-FBI Director Robert Mueller as special counsel to handle the entire Russian Federation investigation Wednesday and answered questions from senators on the decision to do so and the future of that investigation.
Conversations between Mr Flynn and Mr Kislyak accelerated after the Nov 8 vote as the two discussed establishing a back channel for communication between Mr Trump and Russian President Vladimir Putin that could bypass the United States national security bureaucracy, which both sides considered hostile to improved relations, four current U.S. officials said. He also assured the audience at a separate event that, "believe me, there's no collusion".
Nehrona said he understands why the Department of Justice felt that an independent counsel was needed to lead the investigation.
However, US media reported that a top Republican on that panel said it had been advised that Mr Flynn would not honour a subpoena to appear before the committee for questioning.
"Until we have seen the documents, until we have seen some more testimony, I think it is inappropriate to talk about any more conclusions", McCaskill said. Trump muddled the waters further on Thursday, when he again cited Rosenstein's memo as one of the reasons he fired Comey.
-Top members of the Senate Judiciary Committee asked the Federal Bureau of Investigation to provide any Comey memos and asked the White House to turn over any audio recordings that might exist of conversations with the now-fired director.
Democrats disagree. Virginia Sen. He has been tasked with carrying on the investigation that former FBI Director James Comey told Congress about before he was sacked by President Donald Trump.
"Great choice, best man at the best time, and nobody pushes him around", said Bernazzani.