PORTSMOUTH, N.H. — Donald J. Trump descended from a black helicopter emblazoned with his name, strode across the tarmac and stood for 30 seconds until he made sure the cameras were in place.

“You ready?” he said, a confident smile spreading across his face. “Is everybody ready?”

Mr. Trump’s visit to New Hampshire on Wednesday had all the makings of a made-for-television moment well before the White House produced President Obama’s “long-form” birth certificate. But Mr. Obama’s decision to weigh into the debate over the authenticity of his American citizenship added another curious layer of complexity to Mr. Trump’s arrival here.

“I’m very proud of myself because I’ve accomplished something that nobody else has been able to accomplish,” Mr. Trump said. “I am really honored, frankly, to have played such a big role in hopefully, hopefully, getting rid of this issue.”

Yet throughout the day on his inaugural trip to New Hampshire — in this election cycle, at least — Mr. Trump proceeded to keep bringing up the subject, which he has pushed repeatedly in recent weeks in attacking Mr. Obama. He mentioned it in a stop at the Roundabout Diner. He raised it during a private Republican fund-raising luncheon. And he asked factory workers whether they had heard the news.