“You look at all the irregularities, you can come to the conclusion that this is an illicit hearing,” Rudolph W. Giuliani, the president’s personal lawyer, said in an interview. “This is the first time that a president hasn’t had the ability to have his party to call witnesses in the preliminary phase. It sounds like they’re singling him out for unfair treatment.”

Constitutional scholars, though, were not impressed. “It looks like a pathetic attempt to make a legal argument when the president is really expressing rage at the Congress for trying to stop him,” said Corey Brettschneider, an impeachment expert at Brown University. “What’s sad about it is it’s so poorly drafted and the legal arguments are so nonexistent that you wonder who’s advising the president.”

Jack Goldsmith, a Harvard Law School professor and former senior Justice Department official under President George W. Bush, said Mr. Trump’s position was more political than constitutional.

“The White House letter’s legal objections don’t have merit,” he said. “The letter, like the ‘official impeachment inquiry’ itself, is a hardball tactic designed to achieve maximum political advantage” before the public.