The email raises further questions about the process by which Mr. Trump imposed the hold on the military aid, and the link between the hold and the requests he made of Mr. Zelensky in the telephone call, which prompted concern among national security officials with knowledge of the conversation.

In the call, after Mr. Zelensky mentioned Ukraine was ready to buy anti-tank missiles to use in a war against a Russian-backed insurgency, Mr. Trump said, “I would like you to do us a favor though,” according to a reconstructed transcript released by the White House. He then pressed Mr. Zelensky to open an investigation based on a conspiracy theory that Ukraine had interfered in the 2016 United States elections and one based on unsubstantiated claims of corrupt acts by former Vice President Joseph R. Biden Jr., the Democratic presidential candidate.

That call took place from 9:03 a.m. to 9:33 a.m. At 11:04 a.m., Mr. Duffey emailed Defense Department officials telling them of the aid, “Please hold off on any additional DoD obligations of these funds, pending direction from that process.” Obligation refers to the process of a government agency designating how funds will be spent.

In addition, he wrote, “Given the sensitive nature of the request, I appreciate your keeping that information closely held to those who need to know to execute the direction.”

A senior administration official, speaking on the condition of anonymity to publicly discuss the matter, said the timing of the email — an hour and a half after Mr. Trump’s July 25 call with Mr. Zelensky — was coincidental.

The official said the email was part of a weekslong exchange over aid to Ukraine. The July 25 email came after the budget office issued a formal, written hold on the aid, the official said. The reference to sensitivity around the discussions, the official said, was based on the potential for concerns about career officials at the agency that had arisen from previous instances when aid had been cut, as well as the fact that the freeze related to national security matters.