Lev Parnas and wife Svetlana Parnas arrive at federal court on December 2, 2019 in New York City.

Federal prosecutors on Monday said they are "likely" to file new criminal charges in a pending case involving associates of Rudy Giuliani, the personal lawyer of President Donald Trump.

"We think a superseding indictment is likely," said prosecutor Douglas Zolkind during a hearing in U.S. District Court in Manhattan in the case of Giuliani associates Lev Parnas and Igor Fruman, and two other men, Andrey Kukushkin and David Correia.

However, the prosecutor said no firm decision has been made on whether to file additional charges against the men, who are charged with violating campaign finance laws.

"We are continuing to evaluate," Zolkind told Judge J. Paul Oetken.

Parnas and Fruman were helping Giuliani in an effort to get the government of Ukraine to launch investigations into former Vice President Joe Biden and into a conspiracy theory that Ukraine interfered in the 2016 U.S. presidential election.

That effort, and Trump's participation in it, are the subject of ongoing impeachment proceedings against Trump in the House of Representatives.

Parnas was the only one of the defendants present for Monday's hearing. The other men had their presences excused.

Giuliani has not been charged in connection with the case. But The Wall Street Journal reported last month that a federal grand jury in Manhattan has issued subpoenas seeking information about Giuliani's consulting firm.

The subpoenas, which went out to people with ties to Giuliani, "suggest that prosecutors are looking closely at the work of Mr. Giuliani himself, according to people familiar with the matter," the Journal reported.

The newspaper also reported the subpoenas seek materials related to two pro-Trump groups, America First Action and America First Policies.

Zolkind at Monday's hearing gave a rough tally of the amount of material seized in connection with the case since the four men were charged in October.

That material includes records from phones, banks and the Internet obtained from witnesses and companies related to the charges.

Prosecutors have collected thousands of files currently totaling around nine gigabytes of data, Zolkind said.

Much of the information was obtained through subpoenas, and search warrants were issued for access to email and iCloud accounts and physical premises, he said.

"There's additional stuff that's coming," Zolkind said.

He noted that the process of extracting data from seized electronic devices is time-consuming, and that none of the defendants' lawyers have volunteered password information to expedite the process.

In response, Todd Blanche, a lawyer for Fruman, said he had never been asked to provide that information.

Defense lawyers also complained about the large amount of potential evidence they would have to sift through without clarity from the prosecutors about what could be used in a trial.

But Zolkind objected to the request from Kukushkin's lawyer, Gerald Lefcourt, to provide an exhibit list far in advance of the trial.

"We're not playing hide the ball," Zolkind said.

But he argued that a draft exhibit list would be "premature."

Parnas' lawyer Joseph Bondy requested that the court loosen Parnas' tight bail conditions.

Parnas is currently under house arrest and wearing a GPS monitoring device.

Bondy requested he be allowed outside a few hours each day for a few days a week to exercise, spend time with his children and get fresh air.

Prosecutors strongly objected to that proposal.

Zolkind said that Parnas, who was arrested at an airport just outside of Washington, D.C., with a one-way ticket out of the U.S., "presents a significant risk of flight."

Zolkind also cited Parnas' extensive foreign ties — including to at least one wealthy oligarch with a private jet — and the deceitful behavior he is alleged to have engaged in.

And "he is under investigation for additional crimes," Zolkind added.

The judge instructed Bondy to make a request about the condition of Parnas' release to the office that supervises defendants released on bail.

The defendants are scheduled to next appear in court on Feb. 2.