WASHINGTON — President Trump said Thursday that he would leave it to Attorney General William P. Barr to decide whether the special counsel testifies before Congress, a concession of sorts after Speaker Nancy Pelosi declared the country in a “constitutional crisis” over the president’s blanket refusal to cooperate with the Democrats investigating him.

His comments were a seeming reversal, since Mr. Trump wrote over the weekend on Twitter that the special counsel, Robert S. Mueller III, should not be allowed to appear before Congress. Mr. Barr — who refused to testify before the House last week amid a spat over the structure of the hearing — has told lawmakers that he has no objection to Mr. Mueller’s testifying.

In a surprise 45-minute news conference in the Roosevelt Room, his first since the release of the Mueller report, Mr. Trump also said he was “pretty surprised” that his eldest son, Donald Trump Jr., was subpoenaed to testify in front of the Senate about his contacts with Russians during the 2016 presidential campaign.

“My son is a good person,” Mr. Trump said. “My son testified for hours and hours. My son was totally exonerated by Mueller.” The president did not make it clear whether he would fight the subpoena, saying: “We’ll see what happens. I’m just very surprised.”