Comey has received invitations to testify from the Senate Intelligence Committee, the Senate Judiciary Committee and the House Oversight and Government Reform Committee. He has not yet stated publicly that he will appear.
The calls came as Congress began another chaotic day in the wake of news that the Justice Department had appointed Robert Mueller, a former FBI chief, as special counsel to probe possible ties between Trump's team and Russia.
The appointment lifted the pressure on many lawmakers, who found themselves under increasing pressure in the last month to support either an independent commission or special prosecutor to probe the Russia matter. Still, Mueller's appointment does not end the investigations already taking place on Capitol Hill, and lawmakers expressed a firm commitment to continuing their efforts.
Those efforts are taking place against a constantly shifting backdrop of news and controversy involving the Trump White House. Earlier this week, The Washington Post revealed Trump disclosed highly classified information to Russian officials during a meeting in the Oval Office. A day later, The New York Times reported Trump had pressured Comey to drop an investigation into former White House national security adviser Michael Flynn, based on a memo Comey wrote summarizing their meeting.
Congressional committees have sent multiple requests to the FBI and the White House to obtain any records of Trump's conversations with Comey. Among them was the House Oversight Committee, whose chairman appeared on television Wednesday night and disputed whether the Comey memo actually exists.
"I'm not even sure these memos exist," Rep. Jason Chaffetz, R-Utah, said in an interview with Fox News. "I'm not even sure they're real. I just don't know. . . . I do think it's worthy of investigation. I think they should pursue it."
Partisan differences also began to emerge on the matter of the special counsel.
While praising Mueller for being "as good as it gets," Chaffetz said he ultimately disagreed with the Justice Department's decision.
"They shouldn't have actually appointed somebody," he told Fox. "They're feeling the political heat. Maybe they're watching a little too much television and reading too many newspapers and whatnot."
He added that he had not seen "any evidence of actual collusion" between Trump associates and the Russian government.
"Where is the actual crime they think they need a special prosecutor to investigate?" Chaffetz said. "I haven't seen that."
The Senate and House Intelligence committees are the primary centers of investigation into the Russia matter on Capitol Hill. Chaffetz has been criticized for failing to use his power to investigative Trump.
Rep. Elijah Cummings of Maryland, the ranking Democrat on Oversight, called on Chaffetz to subpoena documents from the White House after the New York Times reported Trump's presidential transition team was aware of investigations into Flynn before naming him national security adviser.
"There is no longer any excuse to allow the White House to continue stonewalling," Cummings said Thursday in a statement. "The Chairman either needs to subpoena the White House or let the Committee take a vote."
Cummings elaborated in an interview with MSNBC's "Morning Joe."
"We need to look at the vetting process and how it takes place in the new administrations, whether they're Democratic or Republican," he said. "I'm hoping Chairman Chaffetz and I can work together to get some things done."
Outside of the issue of Congress's investigations, Democrats are expressing concerns about the possibility of improper influence by the Trump administration on Mueller's investigation. Several members of the party, including House Minority Leader Nancy Pelosi of California, said Mueller's appointment must be followed by the creation of an independent commission to oversee its own Russia probe.
Democrats' other pressing concern is the search for Comey's replacement.
"The next FBI director must be someone who is nonpartisan, independent, fearless and unimpeachable," Schumer said Thursday, ruling out a politician for the role. "Anyone who suggests a lack of impartiality should not be considered."
Senate Majority Leader Mitch McConnell, R-Ky., did not mention any of these issues during his morning remarks on the Senate floor, focusing instead on health care.
"The entire Senate Republican Conference has been at work debating ideas and making progress," McConnell said. "I hope our friends on the other side of the aisle will join us in bringing some relief to all these families who desperately need it."
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