The president also wrote that “the Justice Department already ruled that the call was good.” His mention of the Justice Department in his Twitter post appeared to be referring to a decision rendered in early September after a review of the whistle-blower complaint between Mr. Trump and Mr. Zelensky. The department found that Mr. Trump did not violate any campaign finance laws when he pressed the Ukrainian president to coordinate with Mr. Barr on investigations into his political rivals. The Justice Department did not consider or rule on whether the call was good or bad. At the time, the Justice Department also found that the complaint did not need to be shared with Congress.

The president wanted Mr. Barr to personally deliver the message to the news media that Mr. Trump had done nothing wrong, much as he did in a news conference he held shortly before the release of the report by Robert S. Mueller III, the special counsel who investigated Russia’s interference in the 2016 elections, according to a person with knowledge of the events.

It was hardly the first time that Mr. Trump has sought to pressure his chief law enforcement official to defend him more aggressively in the face of what he considered an existential crisis. The president never got over his rage at Jeff Sessions, his former attorney general, for recusing himself from Mr. Mueller’s investigation, and tried repeatedly — and unsuccessfully — to get Mr. Sessions to insert himself into that inquiry on Mr. Trump’s behalf.

And to people close to Mr. Trump, the request was also reminiscent of what he wanted James B. Comey, the F.B.I. director at the time, to say publicly about whether the president was personally under investigation as the bureau looked at a possible conspiracy between the Trump campaign and Russian officials in 2016. Mr. Comey had told the president that he was not personally under investigation, but Mr. Trump wanted the F.B.I. director to publicly clear his name. Mr. Comey declined, which he has said was because he did not want to have to take that declaration back if circumstances changed.