NEW YORK — A Ukrainian-born associate of Rudolph W. Giuliani pleaded not guilty Monday to charges he defrauded investors in a start-up insurance company that claimed to offer fraud-protection services to corporate clients — what prosecutors have called a sham business that was never operational.

Lev Parnas, whose ties to Giuliani became a focal point in President Trump’s impeachment, appeared by video in Manhattan federal court to formally face charges related to the company, Fraud Guarantee. The Florida-based entity was defunct, prosecutors say, when Parnas and his business partner David Correia collected investments ranging between $200,000 and $500,000.

Giuliani was paid $500,000 by Fraud Guarantee for consulting work before teaming with Parnas in what would prove an unsuccessful quest to dredge up information in Ukraine that would damage Joe Biden ahead of the election. The former New York mayor, who as Trump’s personal lawyer is leading the president’s long-shot bid to overturn the election’s outcome, has maintained there was nothing improper about his consulting work or his efforts to undermine Biden’s candidacy — though Giuliani’s activities abroad have drawn the scrutiny of federal prosecutors.

On Monday, U.S. District Judge Paul Oetken said the March 1 trial date that had been scheduled for Parnas and his co-defendants was no longer realistic because of rising coronavirus numbers in New York. Courts here have essentially halted such proceedings as a result, and Oetken said that other cases will probably take priority when trials resume because they involve defendants who have been detained.

A new trial date has not yet been set. Oetken gave the lawyers two weeks to agree on a new schedule. Widespread availability of a coronavirus vaccine may be a determining factor.

Parnas and two other men — Igor Fruman and Andrey Kukush­kin — are set to stand trial together. All are free on bail, though lawyers for each argued Monday that their ability to prepare a defense has been inhibited by the pandemic.

Parnas’s lawyer Joseph Bondy told the judge that his investigator, for instance, cannot be sent to places where case counts are particularly high, such as Florida and Texas. Kukushkin’s lawyer Gerald Lefcourt is based in New York, while his client is in California. Lefcourt said they have “never been in the same room” to discuss evidence.

“It is too dangerous to go to trial now,” Lefcourt said, citing New York’s rise in infections. “I don’t want to be in a courtroom with a mask and taking the subway in this situation.”

Assistant U.S. Attorney Nicolas Roos said that several trials have been conducted in the courthouse recently “without incident.”

Authorities have accused Parnas of lying about how much of his money was at stake in Fraud Guarantee and how much had been collected from others. They allege he used tens of thousands to cover personal expenses while telling his backers that their funds were to be used only for operating costs.

Correia, his former partner in the venture, pleaded guilty in October and admitted he duped investors.

Parnas, Fruman and Kukushkin face unrelated charges stemming from an alleged campaign-finance scheme in which, authorities say, they sought to buy political influence for themselves and foreign actors through donations to political candidates. Prosecutors zeroed in on a $325,000 donation made to a pro-Trump super PAC, America First Action.

The three men intend to contest those charges at trial.

Correia, as part of his plea agreement, admitted he lied to election regulators about the source of the donation. Prosecutors have recommended he serve 3½ years in prison.