Similarly, Mr. Barr recommended that Mr. Trump release the reconstructed transcript of the July 25 call with President Volodymyr Zelensky of Ukraine, arguing that it would show that Mr. Trump did nothing wrong. Pat A. Cipollone, the White House counsel, agreed with that recommendation, but Secretary of State Mike Pompeo argued against releasing the call record, saying that it would hurt American diplomacy if foreign leaders thought their conversations with the president might be made public. Mr. Pompeo was also on the call — which he initially obscured — giving him added reason to not want it publicly aired.

Mick Mulvaney, the acting White House chief of staff, was not included in the discussion and instead was among a number of aides blindsided when he learned that the president had decided to release the reconstructed transcript. In New York with Mr. Trump for meetings at the United Nations, Mr. Mulvaney declared to other aides that he would not be the one defending the call, according to people involved in the matter.

In the run-up to the release of the Ukraine call notes, the White House and the Justice Department exchanged plans for how they would share the information. Mr. Barr said that he could not recall whether Mr. Trump asked him to hold a news conference, according to an administration official. When the Justice Department said it would release a statement rather than hold a news conference saying that it found no campaign finance violation, the White House did not push back, according to an administration official.

To the extent that Mr. Trump was convinced that releasing the reconstructed transcript would clear him of wrongdoing, it was a major miscalculation. The record showed that after Mr. Zelensky talked about his country’s need for more security aid from the United States in the face of Russian aggression, Mr. Trump immediately pivoted and asked him to “do us a favor, though,” and investigate a conspiracy theory about Ukraine’s involvement with Democrats in 2016 as well as Mr. Biden and his son Hunter Biden.

Democrats have seized on that to say it made clear the president was pressing a foreign power for help against his domestic political rivals. In the days that followed, reports emerged about Mr. Barr’s own contacts with foreign leaders for help investigating the origins of the Russia interference investigation. While the Ukraine pressure campaign is separate from the Justice Department’s newest investigation into the 2016 election, critics have said it is more evidence that the Trump administration is trying to carry out work that personally benefits Mr. Trump.

Since the release of the reconstructed transcript, Mr. Trump has grown irked when he sees news coverage asserting that the call was problematic, harkening back to the fact that Mr. Barr was among those who told him it would be wise to release it, according to two people close to the president. One of them said that Mr. Mulvaney has fueled the president’s concerns about Mr. Barr, telling Mr. Trump that it was a mistake to make the document public.

In the call, which took place the day after Mr. Mueller testified before Congress, effectively ending his inquiry, Mr. Trump suggested that Mr. Barr was part of his effort to get damaging information about Democrats. “I will have Mr. Giuliani give you a call and I am also going to have Attorney General Barr call and we will get to the bottom of it,” Mr. Trump told Mr. Zelensky.