President Barack Obama walks to the podium to speak to reporters at Omni Rancho Las Palmas in Rancho Mirage, Calif., Feb. 13, 2016.
Photo by Pablo Martinez Monsivais/AP

Obama: ‘I continue to believe Trump will not be president’

Updated
President Barack Obama on Tuesday reiterated that he doesn’t believe New York businessman Donald Trump will ever be president, saying the American people realize the highest office in the nation “is not a reality show.”

“I continue to believe Mr. Trump will not be president,” Obama said when asked about the 2016 election at the conclusion of the U.S.-Association of Southeast Asian Nations summit in Rancho Mirage, California. “And the reason is because I have a lot of faith in the American people. And I think they recognize that being president is a serious job.”

RELATED: Obama: ‘The Constitution is pretty clear’

“It’s not hosting a talk show or a reality show. It’s not promotion, it’s not marketing. It’s hard. And a lot of people count on us getting it right.”

Trump leads in nationwide polls and won the New Hampshire primary last week. His success comes despite — or because of — controversial statements about immigration from Mexico and a plan to temporarily bar Muslims from entering the U.S.

Trump shrugged off the comments, and said they were “actually a great compliment.”

“You’re lucky I didn’t run the last time when Romney ran because you would have been a one-term president,” Trump said.

2/16/16, 8:38 PM ET

Donald Trump: President Obama 'has done such a lousy job'

On Tuesday evening, Donald Trump reacted to President Obama’s earlier remarks about how Trump would not be the next president. Trump hit back by saying Obama is “…lucky I didn’t run last time…because you would have been a one term president.”

Trump added that Obama “has done such a lousy job as president.”

Obama said the presidency is too important to be left to a candidate without the right temperament or knowledge to deal with other nations.

“It requires being able to work with leaders around the world in a way that reflects the importance of the office, and gives people confidence that you know the facts, and you know their names, and you know where they are on a map, and you know something about their history — and you’re not just going to play to the crowd back home, because they have their own crowds back home, and you’re trying to solve problems,” Obama said.

“And so, yeah, during primaries people vent and they express themselves, and it seems like entertainment, and often lot of times it’s reported just like entertainment — but as you get closer, reality has a way of intruding,” Obama said.

Trump won New Hampshire primarily with a strong 35 percent, compared to the 16 percent Ohio Gov. John Kasich got in his second-place finish. Texas Sen. Ted Cruz came in third with 12 percent.

The latest NBC News/Survey Monkey poll found 56 percent of Republican voters now believe that Trump will be the eventual nominee, up from about 4 in 10 (42 percent) a week ago.

“The American people are pretty sensible, and I think they’ll make a sensible choice in the end,” Obama said.

This story originally appeared on NBCNews.com.

Barack Obama and Donald Trump

Obama: 'I continue to believe Trump will not be president'

Updated