Rather than publicly join the fight against House Democrats pursuing the president, Mr. Barr has remained out of the fray, resisting requests by intermediaries from Mr. Trump to go before the cameras to say no crime had been committed. While Mr. Barr exonerated the president in the spring at the end of the Russia investigation, he has been more reticent in the current matter.

The reluctance hints at a new distance between the two men, according to people who have spoken with them. Mr. Trump, angry with his coverage, is aggravated with Mr. Barr for urging him to release a reconstructed transcript of the telephone call with Ukraine’s president at the center of the impeachment drive. For his part, Mr. Barr was bothered that Mr. Trump on that call lumped him together with Rudolph W. Giuliani, the president’s private lawyer, like interchangeable parts of his personal defense team…

“The easiest read of this is, yes, there’s a limit,” said Harry Litman, who served as a deputy assistant attorney general under President Bill Clinton. “Yes, he will push the envelope, but if it’s not plausible to say there’s no crime, he won’t do it.”