The president had taken off his tie but kept on his jacket — a wardrobe change that for him qualifies as casual Friday — and he was in a happy-hour frame of mind. Expansive, engaging, even at times ebullient, Mr. Trump held forth for an hour, addressing reporters by name and alighting on topics as different as Chinese history and Julius and Ethel Rosenberg.

It was a loose, good-humored side of Mr. Trump that the public rarely sees amid the fusillade of angry speeches and venomous tweets that have characterized the president’s first six months in the White House. And it came to light only because he retroactively put the session on the record, asking a reporter the next morning why she had not quoted his remarks…

“One of the great differences between Trump and more successful politicians, like J.F.K. and F.D.R., is that they would vent their spleen in private, but in public, they would project a more humorous and civilized face,” said Robert Dallek, a presidential historian.