On August 20, Mr. Duffey wrote to Ms. McCusker to notify her that the aid freeze was going to be extended again, long past the deadline when the Pentagon had said it needed the hold to be lifted if it was going to be able to spend all of the money before the end of the fiscal year on Sept. 30.

“It is our intent to add the following footnote to the Ukraine apportionment this afternoon to take effect immediately,” Mr. Duffey said in his email to Ms. McCusker, explaining the technical process the White House was using to impose the aid freeze.

“Mike,” Ms. McCusker wrote back several hours later, to Mr. Duffey and other senior officials at the Office of Management and Budget. “Seems like we continue to talk (email) past each other a bit. We should probably have a call.”

William S. Castle, the principal deputy general counsel at the Pentagon, got involved in the debate, reaching out to the budget office’s top lawyer at Ms. McCusker’s request to question him on the hold. Mark Paoletta, the general counsel at the budget office, sent a lengthy response.

But other than about a dozen words — the greeting and the closing of the email — the entire contents of the response were blacked out before being released under the Freedom of Information Act suit.

“Hi Scott,” the email said, followed by four large blacked out areas of text that the White House declined to make public. “Please let me know if you have any questions, Thanks.”

The White House cited a provision of the Freedom of Information that allows the federal government to withhold “deliberative communications, the disclosure of which would inhibit the frank and candid exchange of views that is necessary for effective government decision-making.”