“As of early August, I heard from U.S. officials that some Ukrainian officials were aware that U.S. aid might be in jeopardy, but I do not know how or when they learned of it,” the anonymous whistle-blower wrote. The complainant said that he learned that the instruction to freeze the assistance “had come directly from the president,” and said it “might have a connection with the overall effort to pressure Ukrainian leadership.”

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Publicly, Mr. Zelensky has insisted he felt no pressure to pursue the investigations sought by Mr. Trump.

“There was no blackmail,” Mr. Zelensky said at a news conference this month. He cited as evidence that he “had no idea the military aid was held up” at the time of his July 25 call with Mr. Trump, when Mr. Trump pressed him for investigations into the Bidens and a debunked conspiracy theory about Ukrainian involvement in the hacking of the Democratic National Committee in 2016.

Mr. Zelensky has said he knew about the holdup of the military aid before his meeting in Poland on Sept. 1 with Mr. Pence, but has been vague about exactly when he learned about it. “When I did find out, I raised it with Pence at a meeting in Warsaw,” he said this month.

In conversations over several days in early August, a Pentagon official discussed the assistance freeze directly with a Ukrainian government official, according to records and interviews. The Pentagon official suggested that Mr. Mulvaney had been pushing for the assistance to be withheld, and urged the Ukrainians to reach out to him.

The Pentagon official described Mr. Mulvaney’s motivations only in broad terms but made clear that the same Ukrainian official, Andriy Yermak, who had been negotiating with Mr. Giuliani over the investigations and a White House visit being sought by Mr. Zelensky should also reach out to Mr. Mulvaney over the hold on military aid.

A senior administration official who spoke on the condition of anonymity to speak publicly about the issue said on Monday that Mr. Mulvaney “ had absolutely no communication with the Ukranians about this issue.”