With driving rain on Monday making golf unappealing, it remained unclear what the president did to enjoy himself. Other presidents, including Mr. Clinton, Mr. Bush and Mr. Obama, brought stacks of books with them on vacation, dutifully reported by aides. Mr. Trump is not known as much of a book reader. Mr. Bush loved clearing brush and bicycling on his ranch, while Mr. Clinton and Mr. Obama liked to play cards. Mr. Trump is not often spotted with a chain saw or a deck of cards.

CNN cheekily contrasted Mr. Trump’s vacation with that of his Russian counterpart, Vladimir V. Putin, who was shown fishing bare chested in Siberia. Mr. Trump is not much of a fisherman nor does he often take his shirt off in public.

He does watch cable television. Around 7:30 a.m. on Monday, Senator Richard Blumenthal, Democrat of Connecticut, went on CNN to talk about the special counsel investigation into possible ties between Mr. Trump’s associates and Russia during and after last year’s election. Mr. Trump presumably was watching, because about 15 minutes later he was flaming Mr. Blumenthal.

“Interesting to watch Senator Richard Blumenthal of Connecticut talking about hoax Russian collusion when he was a phony Vietnam con artist!” he wrote on Twitter. “Never in U.S. history has anyone lied or defrauded voters like Senator Richard Blumenthal. He told stories about his Vietnam battles and conquests, how brave he was, and it was all a lie. He cried like a baby and begged for forgiveness like a child. Now he judges collusion?”

Mr. Blumenthal received at least five deferments from military service during the Vietnam War era and then went into the Marine Reserve, where he served in a unit in Washington. But as a politician, he referred to himself as having “served in Vietnam” or “served during the Vietnam era.” The New York Times article exposing these false or misleading statements in 2010 did not, however, report that he had told stories about Vietnam battles or conquests, nor that he had cried when exposed. Mr. Trump received five deferments from the draft: four for college and one for bad feet.

Mr. Blumenthal responded, using Mr. Trump’s own favorite medium. “Mr. President: Your bullying hasn’t worked before and it won’t work now. No one is above the law,” he wrote on Twitter. “This issue isn’t about me — it’s about the Special Counsel’s independence and integrity.”

Mr. Trump was still stewing about it nine hours later. “I think Senator Blumenthal should take a nice long vacation in Vietnam, where he lied about his service, so he can at least say he was there,” he wrote on Twitter.