"I continue to believe Mr Trump will not be President. And the reason is because I have a lot of faith in the American people, and I think they recognise that being President is a serious job," Obama told reporters after the first ever US-ASEAN Summit in Sunnylands, California.
"It's not hosting a talk show or a reality show. It's not promotion. It's not marketing," he said.
"You're lucky, I didn't run last time when Romney ran because you would have been a one-term president," Trump said at a campaign rally in South Carolina.
Trump also interpreted Obama's prediction as praise after outlining his grievances against the Obama administration's budgets, health care, immigration policies and response to ISIS.
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"He has done such a lousy job as President," Trump retorted at a campaign event in Beaufort, South Carolina. "He's set us back so far, that for him to say that actually is a great compliment."
He said he thinks foreign observers are troubled by some of the rhetoric that is taking place in these Republican primaries and Republican debates.
"I don't think it's restricted, by the way, to Mr Trump. I find it interesting that everybody is focused on Trump, primarily just because he says in more interesting ways what the other candidates are saying, as well," he noted.
"He may up the ante in anti-Muslim sentiment, but if you look at what the other Republican candidates have said, that's pretty troubling, too," Obama said.
In an apparent reference to another Republican presidential aspirant Marco Rubio, the Senator from Florida, Obama said there is a candidate who sponsored a bill, which he supported, to finally solve the immigration problem, and he is running away from it as fast as he can.
Observing that all Republican candidates are denying climate change, Obama said that is troubling to the international community, since the science is unequivocal.