NEW YORK — Federal prosecutors said Monday that they will not attempt to block one of Rudolph W. Giuliani’s associates from cooperating with House impeachment investigators even though a court order says he may not share records related to his criminal proceedings.

A lawyer for Lev Parnas asked for the government’s assistance in allowing him to comply with a House subpoena, noting that many of the phones and electronic devices obtained by search warrant in Parnas’s campaign finance fraud case remain in federal custody and off limits to him.

Assistant U.S. Attorney Douglas Zolkind said earlier in the hearing that law enforcement confiscated 14 phones and devices from Parnas, six of which were in his possession at the time of his arrest in October at Dulles International Airport in suburban Washington. He was traveling with two iPhones, a Samsung device, an iPad and another cellphone, and eight additional devices were taken from his Florida home.

Zolkind told U.S. District Court Judge J. Paul Oetken that the existing protective order on documents in the case controls “any potential desire” to produce materials handed over in the discovery process. “That includes [to] Congress,” the prosecutor added.

But Zolkind said his office would not object to any move by Parnas to ask the judge for permission to provide lawmakers with materials taken in warrant seizures.

Parnas’s lawyer Joseph Bondy asked the judge to compel the government to turn over the phone and computer records more quickly than they have been, so his response to the House can be timely.

Zolkind said the process has been lengthy because of privacy protections on the devices, and that he has repeatedly asked Parnas’s legal team to provide his passwords.

Parnas was arrested along with Igor Fruman, a fellow Soviet emigre. The U.S. attorney’s office in Manhattan has charged them with evading campaign finance laws by filtering foreign political donations through a shell organization they created. The company purported to be an import-export business but was inactive except for the donation enterprise, officials said.

Both men have pleaded not guilty.

Parnas and Fruman allegedly worked with Giuliani, President Trump’s personal attorney, in his attempts to influence the Ukrainian government on behalf of the president. The pair were allegedly seeking information that Giuliani and Trump hoped would discredit former vice president Joe Biden and Biden’s son Hunter, who held a lucrative position on the board of a Ukrainian energy corporation while his father was in office.

The elder Biden is a Democratic candidate for president.

Federal prosecutors are investigating Giuliani’s activities, but the former New York mayor has not been accused of wrongdoing and maintains that his work was aboveboard.

On Monday, the judge rejected a request by Parnas to change the conditions of his house arrest so that he may leave home to exercise and spend time with his children.

Zolkind said that Parnas clearly “presents a risk of flight” given his “extensive” foreign ties.

“In addition to all of that [Parnas is] under investigation for additional crimes,” Zolkind said. “He has a significant incentive to flee” and access to “people who could certainly support him financially if he were to lose the money he put up for bail.”

Earlier in the hearing, Zolkind said it was likely there will be a superseding indictment in this case — meaning that others could face charges — but he offered no details.

“We are continuing to evaluate,” he said.

Federal prosecutors say that Parnas and Fruman tried to establish political connections beginning in March 2018 by working the campaign event circuit, attending fundraisers and functions, and giving considerable donations to various candidates, federal prosecutors allege.

Officials say they gave $325,000 to Trump-aligned super PAC America First in May 2018. The following month, they attended a dinner organized by the group at Trump International Hotel in Washington. The president and son Donald Trump Jr. were at the event, the organization previously confirmed.

Prosecutors have said that Parnas and Fruman sought the help of a congressman in ousting Marie Yovanovitch from her post as the U.S. ambassador to Ukraine by committing to raise $20,000 for the lawmaker. That effort stemmed “at least in part” from a request made on behalf of “one or more” officials in Ukraine, the U.S. attorney’s office said at the time of their arrest.

Finance records have identified former congressman Pete Sessions (R-Tex.) as the recipient of the funds. Sessions, who has been subpoenaed by federal prosecutors in Manhattan, has denied wrongdoing and has expressed willingness to cooperate with the probe.

Yovanovitch, one of several State Department officials to testify in the House impeachment inquiry, was removed from her job in May.