The committee subpoenaed Comey on November 21 to appear for a deposition December 3 regarding his handling of the FBI investigations into Hillary Clinton's use of a private email server and possible collusion between the Trump campaign and Russian government.
Nadler predicted the legal process involved with deciding Comey's challenge could outlast the current Congress and will "run out the clock" on the Republican subpoena.
The court document filed by Comey's team said leaking material would "support a false political narrative, while subjecting the witnesses to a variety of abuse".
In a Monday interview with CNN's Erin Burnett on "Erin Burnett OutFront", Goodlatte rejected Comey's proposition for a public hearing, calling a it "not an appropriate forum" because it could reveal investigative details to other potential witnesses.
Comey and his defense team believe that, because of his prior public and private testimonies given to Congress, Republican lawmakers are attempting to play partisan games.
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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.
A federal judge on Friday delayed a decision on whether to block U.S. House Republicans from compelling former FBI Director James Comey to testify next week in secret about his actions on investigations leading up to the 2016 presidential elections.
By insisting that the interview must be done behind closed doors because of the sensitive information at stake, Kelley added, lawmakers are using the subpoena as "both a sword and a shield" so that they can take "shots at the guy in a dark alley" and "let people see what we want them to see".
Hungar told the judge that such a concern was not warranted because the closed-door deposition was not confidential and anyone, including Comey, could say publicly whatever they pleased about the contents of the meeting.
A Justice Department inspector general report issued earlier this year criticized Comey for his handling of the Clinton matter, but said he did not exhibit political bias.
Comey was first asked to appear before the joint committee voluntarily but declined, resulting in the subpoena.