House impeachment investigators questioned another ex-Trump administration official behind closed doors Wednesday and rebuffed Republicans’ efforts to open up the rapidly accelerating probe, as President Trump warned that the GOP “won’t forget” Democrats’ illegitimate attempt to drive him from office.

Michael McKinley, a former adviser to Secretary of State Mike Pompeo, told House investigators that he quit last week partly because of the president’s campaign against ex-Ukraine ambassador Marie Yovanovitch, whom Mr. Trump criticized in a phone call with Ukrainian President Volodymyr Zelensky, according to people familiar with his testimony.

House Democrats say Mr. Trump abused his power by pressuring Mr. Zelensky to investigate Democratic presidential candidate Joseph R. Biden, an accusation the president heatedly rejects.

In New York, the FBI arrested the fourth man charged in a campaign-finance scheme involving associates of Mr. Trump’s personal lawyer, Rudolph W. Giuliani. Two of the defendants are scheduled to appear in federal court on Thursday.

Mr. Trump intensified his objections Wednesday that Democrats are persecuting him in private with a parade of uninformed witnesses, while ignoring government-orchestrated corruption in the 2016 presidential election that he claims went all the way up to former President Barack Obama.

“I have all these people testifying,” the president said. “I don’t even know these people. I never even heard of some of them, most of them. We’re not allowed to representation. We’re not allowed to lawyers. We’re not allowed to have anything. The Democrats are treating the Republicans very, very badly. And the Republicans won’t forget it because …what the Democrats are doing to this nation is a disgrace.”

Hillary Clinton called Ms. Yovanovitch and former White House National Security Council aide Fiona Hill, who both testified against the president, “gutsy women.”

Republicans stepped up their criticism of the partisan probe but made no headway. House Freedom Caucus Chair Andy Biggs, Arizona Republican, and a handful of other GOP lawmakers were denied entrance Wednesday to the secure room where the impeachment inquiry has been underway.

They demanded to see the transcript of former Envoy to Ukraine Kurt Volker’s testimony from last week and for access to the closed-door hearings, a demand that was also denied.

“This is an insane asylum and the inmates are running it,” said Rep. Louie Gohmert, Texas Republican.

The president said he is eagerly awaiting a report from a Justice Department inspector general’s investigation into the origins of the FBI’s counterintelligence probe of the Trump campaign in 2016. That investigation, which turned into special counsel Robert Mueller’s long-running probe, found no collusion between the campaign and Russia’s meddling in the election.

“It was a corrupt election,” Mr. Trump said at a White House press conference. “Maybe it goes right up to President Obama. I happen to think it does.”

Earlier, Mr. Trump said there is “nothing wrong” with Mr. Giuliani investigating U.S. election corruption that he believes originated in Ukraine.

Warning that Democrats’ impeachment effort will come back to haunt them, Mr. Trump told reporters at the White House that Mr. Giuliani “was seeking out corruption” in his probe and his discussions with Ukraine officials.

“There’s nothing wrong with seeking out corruption,” Mr. Trump said. “People want to find out, why was it so corrupt during that [2016] election? And I want to find out more than anybody else.”

As more administration officials rejected congressional subpoenas this week, House Majority Leader Steny Hoyer said Democrats would take them to court to force them to comply. Mr. Hoyer’s comments came just a day after key officials from the administration — Vice President Mike Pence, Secretary of Defense Mark T. Esper and acting OMB Director Russell Vought — as well as Mr. Giuliani refused to cooperate with Democrats.

“Let me tell you, Mr. Giuliani will be held accountable to the government, as we will hold every other individual,” Mr. Hoyer said.

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