NEW BERN, N.C. — In this gracious riverfront town, where the waters rose with frightening swiftness last week to submerge entire neighborhoods, President Trump gazed in wonder on Wednesday at an elegant yacht that had been washed ashore during Hurricane Florence and now lay shipwrecked against the back deck of a red brick house.

“Is this your boat?” Mr. Trump asked the homeowner.

When the man shook his head and said “No,” the president turned with a grin and replied, “At least you got a nice boat out of the deal.”

It was an offhand, if telling, moment on the first leg of Mr. Trump’s trip to the storm-tossed Carolinas — a day in which he found a young apprentice to help hand out box lunches, commiserated with storm victims about their insurance claims, and inspected a landscape rudely transformed by howling winds, historic rains and swollen rivers.

Where other presidents have treated natural disaster tours as dignified, even grave affairs, Mr. Trump has deployed sardonic humor, a candidate’s pep-rally enthusiasm and a real estate developer’s talent for always finding a silver lining. Occasionally, as when he tossed rolls of paper towels to storm victims in Puerto Rico last October, he has gone badly off-key.