WASHINGTON—Two donors to a pro- Trump fundraising committee who helped Rudy Giuliani’s efforts to investigate Democrat Joe Biden were arrested late Wednesday on criminal charges stemming from their alleged efforts to funnel foreign money into U.S. elections and influence U.S. politics on behalf of at least one unnamed Ukrainian politician. In an indictment unsealed Thursday, federal prosecutors in Manhattan alleged Lev Parnas and Igor Fruman were engaged in political activities in the U.S. on behalf of one or more Ukrainian government officials—including a lobbying campaign, targeted at a Republican congressman, to remove the U.S. ambassador in Kyiv. President Trump ordered the ambassador, Marie Yovanovitch, removed from her post in May. The two men were charged with four counts, including conspiracy, falsification of records and lying to the Federal Election Commission about their political donations, which included a $325,000 donation through a limited liability company to a super PAC formed to support Mr. Trump, according to the indictment. Geoffrey Berman, the U.S. attorney in Manhattan, said Thursday the investigation was continuing. Messrs. Parnas and Fruman, both Florida businessmen who are U.S. citizens born in former Soviet republics, made a brief appearance in federal court in Virginia Thursday, dressed in T-shirts. They were arrested at Dulles International Airport on Wednesday while awaiting an international flight with one-way tickets, according to people familiar with the matter. John Dowd, a former lawyer for Mr. Trump who now represents Messrs. Parnas and Fruman, didn’t respond to a request for comment. Mr. Dowd has previously told Congress that the two men were assisting Mr. Giuliani “in connection with his representation of President Trump.” Messrs. Parnas and Fruman have assisted Mr. Giuliani’s effort to investigate Mr. Biden’s son that is now at the center of an impeachment inquiry being conducted by House Democrats. “I don’t know those gentlemen,” Mr. Trump said Thursday when asked about the new charges, adding he hadn’t discussed them with Mr. Giuliani, a former New York City mayor who is serving as Mr. Trump’s private lawyer. However, Messrs. Parnas and Fruman had dinner with Mr. Trump at the White House in early May 2018, shortly before they donated to the pro-Trump super PAC, according to since-deleted Facebook posts captured in a report published by the Organized Crime and Corruption Reporting Project, a nonprofit U.S.-based media organization. Mr. Trump also said he hoped Mr. Giuliani wouldn’t be indicted. U.S. prosecutors announced charges against two Soviet-born donors to a pro-Trump fundraising committee who helped Rudy Giuliani’s efforts to investigate Democrat Joe Biden. Booking photos above of Lev Parnas, left, and Igor Fruman by Alexandria Sheriff’s Office Mr. Giuliani said Thursday that Messrs. Parnas and Fruman were headed to Vienna, Austria, on Wednesday evening for reasons related to their business. He said the two men had also left the country about two weeks ago and had traveled to Vienna between three and six times in the last two months. He said he had been scheduled to meet with the two when they were to return to Washington within days. A law firm run by Joe DiGenova and Victoria Toensing, two lawyers close to the president, hired Mr. Parnas in July to serve as an interpreter related to their representation of Dmitry Firtash, a Ukrainian oligarch, who was detained in Vienna in 2014 on corruption charges filed in the U.S. Mr. Parnas wasn’t set to travel to Vienna on Wednesday in connection to that case, Mr. DiGenova said. A federal prosecutor told a judge the government remains concerned that the men might flee. Attorneys on both sides said they would reach an agreement about the conditions of their bail and would return to the judge soon. Their political giving—aimed at Republicans—was funded in part by an unnamed Russian donor, the indictment alleges. Federal law bans foreigners from contributing to U.S. elections. A limited liability company created by the men was used to disguise the source of some of the money, the indictment alleges. Since late 2018, Messrs. Fruman and Parnas have introduced Mr. Giuliani to several current and former senior Ukrainian prosecutors to discuss the Biden case, acting as key conduits of information. In July, Mr. Parnas accompanied Mr. Giuliani to a breakfast meeting with Kurt Volker, then the U.S. special representative for Ukraine negotiations. During that breakfast, Mr. Giuliani mentioned the investigations he was pursuing into Mr. Biden and 2016 election interference, according to Mr. Volker’s testimony to House committees. The two had lunch with Mr. Giuliani at the Trump International Hotel in Washington on Wednesday, according to a person who was in the hotel and saw the three together.