Washington (CNN) Attorneys for former FBI Director James Comey and the US House of Representatives fought in court Friday afternoon over whether Comey must testify to Congress in a private hearing next week.

While Comey technically seeks to pause or kill the subpoena, he is using the case to air his accusation that members of the Republican-led House and Senate selectively leak details for their own benefit when they call witnesses to testify in private.

Judge Trevor McFadden said at the hearing that he hoped to rule Monday morning after meeting again with both legal teams.

The meat of Friday's dispute was how each side characterizes Comey's congressional subpoena. Comey's team says Congress is in violation of its own rules by not conducting its fact-finding hearing in public. The hearing won't require that level of secrecy because no sensitive law enforcement information is expected to be discussed, Comey's team said.

The House general counsel countered that because Comey's testimony would be a deposition with staff, a public session isn't required.

McFadden asked whether Comey could release a transcript of his testimony to get the full picture before the public. But Comey's lawyers said that would take too much time, allowing leaks of the information before Comey could release his full testimony.

When McFadden asked Comey's attorney whether he agreed with the House that a judge has never limited Congress in this way before, the lawyer David Kelley responded, "Here's your opportunity, Judge."

Comey has said he would like to testify publicly about the separate investigations into Hillary Clinton's email practices and Russian interference in the 2016 election -- in front of live TV cameras as he has done before.

"The broader purpose of these tweets and leaks appears to be to mislead the public and to undermine public confidence in the FBI and the DOJ during a time when President Trump and members of his administration and campaign team are reported to be under investigation by Special Counsel Robert Mueller and other law enforcement authorities," Comey wrote in his complaint. He says he is a "victim" of Congress' "unauthorized and abusive tactics."

Comey did not attend Friday's hearing in person.

He has asked the judge to issue an emergency order to pause the congressional proceedings and to quash the subpoena. In theory, Comey could lose his court challenge and still win what he's seeking, if he manages to convince the judge to pause his subpoena until the House flips to Democratic control at year's end.

Kelley acknowledged as he emerged from the hearing that it's "an unusual case."

"It's an unusual case, an important case and it's a challenge for all of us to deal with some pretty weighty issues that really haven't been dealt with before," he said.

Kelley refused to answer questions about whether Comey will show up on Capitol Hill for the closed-door interview, now scheduled for Tuesday.

He said Comey "is opposed to the process being used here that is a clear abuse of the legislative process."

He added, "Surely, Congress has an important oversight function, but here they're not really serving a legitimate legislative purpose, which is demonstrated by the way they've done this in the shadows."

The case initially was set to be heard by Judge Timothy Kelly, a Trump appointee, then was reassigned randomly to McFadden, also a Trump appointee, after Kelly likely recused from the case.

Ex-AG Lynch not expected to appear on Hill next week

Former Attorney General Loretta Lynch, who also was subpoenaed by the House Judiciary Committee to appear behind closed doors on Tuesday, is negotiating with the committee to appear at a later date, according to two sources familiar with the discussions, who say the Obama appointee is not expected to appear next week.

Lawyers for Lynch have declined to comment.

Unlike Comey, Lynch has not so far taken legal action to try to quash the subpoena to appear before the committee in private.

This story has been updated.