President Trump said Thursday he knows nothing about two Ukraine-born Florida businessmen, linked to his personal attorney Rudolph W. Giuliani, who have been indicted on charges of funneling cash from a Russian donor to his reelection campaign.

“I don’t know those gentlemen,” Mr. Trump told reporters at the White House as he departed for a campaign rally in Minnesota. “I don’t know what they do. We have nothing to do with this.”

But the president said there might be photographs of him with the pair because he often poses for pictures with people.

Lev Parnas and Igor Fruman were indicted late Wednesday on charges of conspiring to funnel money from a Russian donor to Republican election campaigns in the U.S., including $325,000 last year to America First Action, a pro-Trump super PAC. Two other men, David Correia and Andrey Kukushkin, also face charges.

Mr. Parnas and Mr. Fruman introduced Mr. Giuliani to a Ukrainian prosecutor to investigate former Vice President Joseph R. Biden, a Democratic presidential candidate, and his son Hunter, who was on the board of directors of a Ukrainian gas company.

Shortly after the U.S. attorney for the Southern District of New York announced their indictments, the Democratic House committee chairmen leading the impeachment inquiry into Mr. Trump issued subpoenas for Mr. Parnas and Mr. Fruman.

House Democrats also subpoenaed Energy Secretary Rick Perry for Ukraine-related documents as part of their expanding impeachment inquiry. The chairmen of the House Permanent Select Committee on Intelligence, Foreign Affairs, and Oversight and Reform committees said Mr. Perry has until Oct. 18 to comply.

The inquiry focuses on an anonymous whistleblower’s complaint saying Mr. Trump pressured Ukrainian President Volodymyr Zelensky in a July 25 phone call to investigate the Bidens. Mr. Trump was withholding military aid for Ukraine at the time, but Mr. Zelensky said Thursday that he didn’t know the money was being blocked temporarily at the time of their phone call.

“There was no pressure or blackmail from the U.S.,” Mr. Zelensky told reporters during a marathon press conference. “I had no idea the military aid was held up.”

Mr. Trump said the Ukrainian leader’s account should kill the Democrats’ impeachment inquiry.

“That should be ‘case over,’” Mr. Trump said. “There shouldn’t be any further questions.”

He insisted again that he had done nothing wrong and said Democrats were wasting their time demanding documents and testimony from administration officials.

“How many people can [Democrats] talk to? We had a simple conversation,” Mr. Trump said. “The whistleblower, who seems to be a Democrat that’s involved with a lot of people, gave a false interpretation of the conversation. So I don’t know why they’d be calling Rick Perry. I don’t know why they’d be calling all these people. It’s a very bad situation for our country. You have to run a country. I just don’t think you can have everybody testify.”

Citing Chairman Adam B. Schiff’s made-up version of his phone call at a House intelligence committee hearing, the president said, “What he did is criminal. The Democrats have committed crimes.”

In his first campaign rally since Democrats announced their impeachment inquiry, Mr. Trump told supporters in Minneapolis on Thursday night that “from Day One, the wretched Washington swamp has been trying to nullify” his election.

“They know they can’t win the 2020 election, so they’re pursuing the insane impeachment,” Mr. Trump said. “They want to erase your vote like it never existed. They want to erase your voice and erase your future. But they will fail because in America, the people rule again.”

The president also referred to a report Thursday evening in the Washington Examiner that the anonymous whistleblower who launched the impeachment inquiry against him had worked with Mr. Biden in the White House.

“In a brand new report, just came out as I’m walking on the stage, hard to believe, actually, it turns out that [when] Joe Biden was vice president, he worked with the so-called whistleblower,” Mr. Trump said. “This is nothing but a partisan witch hunt, sabotage. And I’m sure [the media] are going to say it’s a totally unsubstantiated story.”

The president mocked Hunter Biden’s profiteering several times and said of him, “Your father was never considered smart. He was never considered a good senator. He was only a good vice president because he understood how to kiss Barack Obama’s ass.”

Mr. Trump was visiting the district of Somali-born Rep. Ilhan Omar, a left-wing Democrat with whom he has feuded. He called her “an America-hating socialist” who “has a history of launching virulent, anti-Semitic screeds.”

“She is a disgrace to our country, and she is one of the big reasons that I’m going to win and the Republican Party is going to win Minnesota in 13 months,” the president said.

Mr. Trump also boasted of his crackdown on refugee resettlements, telling Minnesotans that “leaders in Washington brought large numbers of refugees to your state from Somalia without considering the impact on schools and communities and taxpayers. I promised you that as president, I would give local communities a greater say in refugee policy and put in place enhanced vetting and responsible immigration controls. And I’ve done that. Since coming into office, I have reduced refugee resettlement by 85%.”

Mr. Parnas and Mr. Fruman face four charges including conspiracy, falsification of records and lying to the Federal Election Commission about political donations. The charges against the pair appear to be unrelated to their Ukraine activities.

Both men have donated heavily to Republican campaigns, including the contribution to America First Action in May 2018 through a business called Global Energy Producers, according to FEC data.

Prosecutors say the two men shielded the foreign source of the funds by laundering through their U.S. business. Mr. Fruman went so far as to intentionally misspell his name so the FEC wouldn’t catch the donations, they said.

They were arrested at Washington Dulles International Airport before they could board an international flight with one-way tickets, said Geoffrey Berman, U.S. attorney for the Southern District. The men were seen earlier Wednesday having lunch with Mr. Giuliani at the Trump International Hotel in Washington, The Wall Street Journal reported.

The complaint says the men took part in political activities in the U.S. on behalf of at least one Ukrainian government official, including an effort to remove the U.S. ambassador in Kyiv, Marie Yovanovitch, who was recalled from her post in May.

The pair reportedly pledged to raise campaign funds for then-Rep. Pete Sessions, Texas Republican, and met with him at a pro-Trump super PAC event in 2018. Mr. Sessions is not charged but is referred to as “Congressman-1” in the indictment.

They also have claimed to have attended a small gathering with the president in Washington in May 2018 focused on the midterm elections.

The House committees are demanding that the two men testify and turn over documents related to efforts to get Ukrainian officials to investigate the Bidens, the Democratic National Committee or Hillary Clinton.

“Your clients are private citizens who are not employees of the executive branch,” the committee chairmen wrote in a letter to Mr. Giuliani. “They may not evade requests from Congress for documents and information necessary to conduct our inquiry.”

The federal investigation stemmed from a complaint filed by the Campaign Legal Center, an open government advocacy group. The organization uncovered the Trump campaign donation in July 2018.

“We are pleased that federal law enforcement has conducted an investigation into these campaign finance crimes and made these two arrests. The public is now learning just how dangerous dark money can be in U.S. elections, including the potential for illegal foreign funds, which DOJ says were used here,” said Trevor Potter, president of the Campaign Legal Center and former Republican chairman of the FEC.

“The fact that these two individuals were working with Giuliani and Ukrainian government officials to alter U.S. policy in that country will obviously be relevant to the impeachment investigation,” Mr. Potter said.

In issuing a subpoena to Mr. Perry, the Democratic committee chairmen said recent media reports “have raised questions about any role you may have played in conveying or reinforcing the president’s stark message to the Ukrainian president.”

“These reports have also raised significant questions about your efforts to press Ukrainian officials to change the management structure at a Ukrainian state-owned energy company to benefit individuals involved with Rudy Giuliani’s push to get Ukrainian officials to interfere in our 2020 election,” the chairmen added.

The president also confirmed that former Rep. Trey Gowdy, South Carolina Republican, won’t be able to join his legal team as outside counsel in the impeachment defense until at least January because of what he called “lobbying rules.”

• Gabriella Muñoz contributed to this report.

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