"It is my strong recommendation that the Judiciary Committee investigate all issues that raise a question of obstruction of justice", the California Democrat wrote in a letter to Senate Judiciary Chairman Chuck Grassley on Friday.
"At some point, the Judiciary Committee has to decide whether it's going to continue to be a serious committee", Sen.
A Justice Department official told CNN on Sunday that any testimony from Sessions on Tuesday would likely be in a closed hearing, but the intelligence panel still needs to make a final determination.
Grassley's office did not immediately respond to CNN's request for comment.
The Senate Judiciary Committee has been working to obtain the memos and any possible White House recordings of Comey's interactions with President Trump. "The American people deserve answers".
Columbia University Law School professor Daniel Richman reportedly went into hiding this week after former Federal Bureau of Investigation director James Comey revealed that he gave his "contemporaneous" memo of his interactions with President Donald Trump to Richman and asked Richman to leak it to the New York Times.
"The FBI being our responsibility most of it will deal with the FBI and anything the FBI got to do with Russian Federation and anything else that has been brought up because of Comey's testimony before the committee", Grassley said of what he wanted his committee to investigate. Comey told the Senate committee that he hoped the leak would lead to the appointment of a special counsel.
In the letter, Feinstein told Grassley she is "concerned" about Director of National Intelligence Dan Coats' and National Security Agency Director Admiral Rogers' refusals to answer questions from senators, adding that she wants to determine whether Trump asked Coats or Rogers "to take any action" on the Russian Federation investigation.
In his testimony, Comey said he was uncomfortable when Lynch asked him to refer to the investigation as a "matter" instead of an investigation and cited her now-infamous tarmac meeting with former President Bill Clinton as a red flag. Four congressional committees have appealed directly to Comey and the Department of Justice to obtain the memos for review but have not yet obtained them. "I think we need to know more about that, and there's only one way to know about it, and that's to have the judiciary committee take a look at that".
"I would have a queasy feeling too", Feinstein said.