Presumptive Republican presidential nominee Donald Trump Donald John TrumpUS reimposes UN sanctions on Iran amid increasing tensions Jeff Flake: Republicans 'should hold the same position' on SCOTUS vacancy as 2016 Trump supporters chant 'Fill that seat' at North Carolina rally MORE said it's an "honor" that President Obama has been calling him out lately.

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When asked about Obama's attacks in an interview with Fox News's "Hannity" Wednesday night, Trump said that he had come close to running against the president in 2012, but ultimately decided against it. He added that a friend had told him that Obama was privately worried about the prospect of facing Trump in an election.

"I don't know if that was a good decision or a bad decision," he said. "I think it was actually — I think we're going to do great this time. I think I would have beaten him last time, frankly, had I decided to run."

"I'm definitely on his mind. I mean every time he speaks, he mentions my name, which is an honor. I think it's probably not a bad thing," Trump added.

Obama has been an outspoken critic of the Republican presumptive nominee's rhetoric and took aim at him during a commencement speech at Rutgers University on Sunday.

"Facts, evidence, reason, logic and understanding of science, those are good things," Obama said. "These are qualities you want in people making policy.

"We traditionally have valued those things, but if you were to listen to today's political debate, you might wonder where this strain of anti-intellectualism came from," Obama said. "So, class of 2016, let me be clear as I can be: In politics and in life, ignorance is not a virtue. It's not cool to not know what you're talking about."

Trump lashed out at Obama in a tweet a few days later, calling him "the worst president in U.S. history," a claim he repeated in the Wenesday interview.