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.

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.

Separately, hours after the indictment became public, three Democratic-controlled House committees leading the impeachment probe of Mr. Trump issued subpoenas to Messrs. Parnas and Fruman for documents. An attorney for the two men had said in an Oct. 8 letter to the committee that it would take time to gather documents and that the two wouldn’t be available for depositions originally scheduled for this week.

While the two men assisted Mr. Giuliani in investigating Mr. Biden and his son Hunter, they also solicited money from Ukrainians while touting their connections to Washington, according to people familiar with their activities in Ukraine.

Mr. Giuliani identified the two men in May as his clients. On Thursday, he said he wasn’t representing them in this case. Mr. Giuliani said Thursday morning he hadn’t been contacted by federal prosecutors in Manhattan. Jay Sekulow, a lawyer for Mr. Trump, said: “Neither the president nor the campaign nor political-action committees were aware of these transactions.”

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.