Chairman Chuck Grassley and the panel's top Democrat, Dianne Feinstein, plan to move forward on their inquiry, which will look into Russia meddling in the elections as well as whether there was any improper political interference with the FBI under both Trump and former President Barack Obama's administration.
"I think there's general agreement," Feinstein told CNN on Monday. "I think the important thing is to get started. What I found in these investigations is when you do them, you look at things you need to look at in addition."
Leaders of the Senate intelligence committee have suggested that investigating whether Trump obstructed justice will not be a main focus of their investigation
, which is primarily aimed at reviewing Russian efforts to sway last year's election to Trump.
That means that the judiciary panel could be the main body in Congress to investigate whether Trump improperly used his authority to urge Comey to back off an investigation of his former national security adviser, Michael Flynn.
Asked if exploring obstruction under Trump would be part of the probe, Feinstein said, "I think whether it includes it or not, people look for it. That will be the result. ... You look at various pieces of information, you see something and say, 'Woah."
A Grassley spokesperson agreed with Feinstein's comments, saying the two sides are in "general agreement" on the scope of the inquiry.
Robert Mueller, the Justice Department special counsel investigating Russian interference in the 2016 election, is expected to meet with committee leaders Wednesday.
Sen. Richard Blumenthal, a Democrat on the committee, said Monday on CNN's "Erin Burnett OutFront" that "obstruction of justice has to be included" in the investigation, and critiqued Jay Sekulow, a lawyer for Trump who has dismissed the idea the President could have obstructed justice by firing Comey.
"Political interference with an ongoing investigation, regardless of what the President's lawyer may say, could make the President a target, a subject, a person of interest," Blumenthal said. "So our hearing will very much involve potential obstruction of justice in the firing of Comey and other actions."
The two leaders of the panel have both been frustrated that key witnesses have testified before the Senate intelligence committee -- rather than their panel -- and both have warned that Comey in particular could face a subpoena if he does not agree to testify before Judiciary. In an interview with CNN last week, Grassley suggested he would be on board with issuing subpoenas for Comey and other witnesses to testify before his panel.
Asked last week if he was open to investigating the White House on questions of obstruction of justice, Grassley did not rule it out.
"I think I better wait until I get done with my conversations with Feinstein before I answer that question," said Grassley, who also wants to review any actions taken by Obama attorney general Loretta Lynch to influence the Clinton email investigation. Comey was among those critics who cited Lynch's June 2016 tarmac meeting
with former President Bill Clinton as a sign the Justice Department was not capable of an independent investigation into Hillary Clinton.