Comey argued in the lawsuit that a private interview with House committee staffers would open him up to selective leaks that could misrepresent his testimony, and Kelley echoed that in court on Friday afternoon.
Republican lawmakers have also summoned former Attorney General Loretta Lynch to testify in a closed-door session.
Comey has said he'd be willing to speak to lawmakers but would push that such testimony be made in public.
'Today my legal team filed court papers to try to get transparency from House Republicans.
"Let the American people watch", Comey tweeted on Thursday evening.
The subpoena ordering Comey's testimony was issued as part of a joint investigation by the House Judiciary Committee and House Oversight Committee into decisions made by the FBI in connection with its investigation into former Secretary of State Hillary Clinton's use of a private e-mail server and its investigation into whether President Donald Trump's campaign colluded with Russian Federation.
The filing cites what it calls the "abusive pattern of the selective leaking" by the joint committee.
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They said House committees had been leaking to "support a false political narrative, while subjecting the witnesses to a variety of abuse".
The fired Federal Bureau of Investigation official revealed over Thanksgiving that he was subpoenaed by lawmakers and demanded he be given the opportunity to testify in public on December 3rd, citing past instances of "leaking and distortion" of testimonies by House Republicans.
CNN has reached out to Goodlatte for comment on Thursday's filing. He needs to appear before the Committees, as all other witnesses have done.
The legal maneuver by Comey is not unheard of in Washington probes, but it's not always successful, according to Eric Schickler, a professor of political science at the University of California, Berkley.
Kelly, one of three Comey defense attorneys present in court in lieu of Comey himself, argued that the House would have to issue a new subpoena should the date be moved.
Judge Trevor McFadden, who was appointed to the U.S. District Court for the District of Columbia by President Donald Trump, said he wanted to review the case over the weekend before making a ruling and scheduled a follow-up hearing for Monday at 10 a.m.