NEW YORK — A Ukrainian-born businessman with ties to President Trump's personal lawyer may remain on house arrest until his criminal case is resolved, a federal judge said Tuesday, rebuffing prosecutors who labeled him a flight risk with access to money and powerful connections overseas.

Prosecutors cited Lev Parnas’s foreign ties, including to a Ukrainian oligarch who is fighting extradition to the United States, where he is charged in a bribery case, in their failed bid to have Parnas returned to jail pending trial.

Parnas was arrested in October along with another associate of Rudolph W. Giuliani, the president’s lawyer, and charged with violating campaign finance laws. Both men have pleaded not guilty.

Authorities have highlighted a “suspicious” $1 million transfer made in September from a Russian bank account — funds, prosecutors alleged, that Parnas hid from them as he gave conflicting accounts about his personal assets. It was disclosed in court Tuesday that the funds were transferred by a lawyer for Dmytro Firtash, the Ukrainian oligarch, as a loan to Parnas’s wife.

The lawyer, Ralph Isenegger, said in a statement that he agreed in August to loan Parnas and his wife $1 million so they could purchase a home in Florida. He called the arrangement a “personal business transaction” that was not undertaken at the request of his client Firtash. Isenegger said he used his own money for the loan, which he told no one else about at the time.

Firtash is living in Vienna. He is represented in the United States by a husband-and-wife legal team who are close to Trump and Giuliani. As The Washington Post reported previously, they asked Attorney General William P. Barr to intercede in the case, but Barr declined.

Prosecutors described Firtash as a benefactor for Parnas, who worked with the oligarch’s lawyers as an interpreter before a fallout apparently involving House Democrats’ plans to impeach the president. Parnas’s attorney, Joseph Bondy, said Firtash has severed his relationship with Parnas, citing Parnas’s willingness to cooperate with Democrats.

“Mr. Parnas has almost no continuing relationship with Mr. Firtash,” Bondy said in court. “ . . . He’s burned those bridges by stating his intent to comply with [a congressional] subpoena.”

Assistant U.S. Attorney Rebekah Donaleski told the judge, J. Paul Oetken, that the $1 million transfer was clearly intended for Parnas, not his spouse.

“It’s an unsecured, undocumented loan to a housewife with no assets,” Donaleski said. “That makes no sense, your honor.”

But the judge said Parnas’s differing accounts of his own assets came with logical explanations. The statements to authorities “might have violated the spirit of what was requested,” Oetken said, but he did not think it amounted to “intentional misstatements warranting the revocation of bail.”

Outside the courthouse, Bondy stood beside his client and said he was “happy we got a fair audience in court.” He said he looks “forward to defending this matter in court and also in continuing to have Mr. Parnas speak his truth to Congress on behalf of all of us.”

Parnas and co-defendant Igor Fruman were arrested in early October at Dulles International Airport outside of Washington. They were intercepted by authorities while preparing to board a flight to Vienna.

Parnas and Fruman are accused of illegally funneling foreign money to political organizations and candidates, hoping to buy influence, according to prosecutors.

Giuliani has said he sought Parnas’s help investigating former vice president Joe Biden, a political rival of Trump’s and a contender for the 2020 Democratic nomination for president. The former New York mayor is not named in the indictment charging Parnas and Fruman, but people familiar with the matter have said he is under investigation by federal prosecutors there.

Prosecutors have said Parnas is a flight risk because of his access to money and his ties to Ukraine and Russia. He potentially faces additional charges, too, another factor that could drive him to try to leave the country, prosecutors have said.

His lawyers said Monday that Parnas would not go back to Ukraine because people there have threatened him.

Shortly after Parnas and Fruman were arrested, Chicago prosecutors handling the Firtash case alerted their counterparts in New York that they had previously run across the pair in their work. They indicated that they believed there might be a broader relationship among all three — beyond Parnas’s work as an interpreter. In court papers, prosecutors have said Parnas earned $200,000 between August and September for the interpreting work. The $1 million loan from the Firtash lawyer came on top of those fees.

Firtash was charged in Chicago in 2013, accused of bribing Indian officials related to mining interests in that country. He was arrested in Austria the following year at the request of American officials, but was released on $172 million bond and has been living in Vienna while fighting extradition.

In a 2017 court filing, prosecutors alleged that Firtash had ties to the “upper echelons” of Russian organized crime. Firtash has denied wrongdoing in the Chicago case and said he does not have any organized crime ties.

In June, the Austrian supreme court ruled against Firtash, paving the way for his extradition to the United States, but he has made last-minute arguments to Austrian courts that have delayed the process.

The following month, Firtash fired his longtime U.S. lawyer Lanny Davis, an ally of Hillary Clinton, and replaced him with husband-and-wife lawyers Victoria Toensing and Joe diGenova, who then hired Parnas to act as an interpreter. The couple quickly secured a meeting with the attorney general, who has informed Firtash’s legal team that he does not plan to intercede and that the case will proceed in Chicago.

Helderman reported from Washington. Tom Hamburger contributed to this report.