"Under our rules on our committee, if Sen. [Dianne] Feinstein [D-Calif.] would agree to subpoena, I would," Grassley, the chairman of the committee, told CNN on Wednesday.

A spokesman for Feinstein said later Wednesday that she supports subpoenaing Comey to testify before the Judiciary Committee.

Comey is scheduled to testify before the Senate Intelligence Committee on Thursday, making his first public comments since he was fired by President Trump last month. His opening statement was released Wednesday ahead of his hearing, providing meticulous details of his past conversations with Trump.

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But members of the Judiciary Committee are continuing to demand that Comey also come before their panel, which has oversight of the FBI.

"I hope Comey will come to the Judiciary Committee after he comes to Intelligence," Schumer told reporters during a weekly leadership press conference.

The two committees are conducting separate investigations into Russia's election meddling, including potential ties between Trump officials and Moscow. They've recently made a series of overlapping requests, including that Comey appear before their committees.

Feinstein told PBS after Comey declined the Judiciary Committee's invitation that she believed he still needed to testify before the panel.

“I think we perhaps need to do more than just invite [Comey]. I think it’s important that he come before the Oversight Committee ... and at least do us the courtesy of appearing and that we should be able to look at his material and ask questions about them,” Feinstein told PBS.

Updated: 5:37 p.m.