In an interview with Today's Savannah Guthrie at the White House, the outgoing president said, "It is the nature of democracy that until those votes are cast and the American people have their say, we don't know."
Just six month earlier, he told Today's Matt Lauer, "I'm pretty confident that the overwhelming majority of Americans are looking for the kind of politics that does feed our hopes and not our fears. You know, talk to me if he wins."
Since those comments on the eve of his State of the Union address on Jan. 13, Trump has claimed the Republican nomination and leads in some polls after the party's convention last week.
Obama, who has supported Democratic nominee Hillary Clinton, will address his party's convention Wednesday evening.
Obama has said Trump is not qualified to be president.
When asked if he was personally frightened by the possibility of Trump having access to nuclear codes, he said, "What I think is scary is a president who doesn't know their stuff and doesn't seem to have an interest in learning what they don't know," Obama said.
"I think if you listen to any press conference he's given, or listen to any of those debates, basic knowledge —about the world or what a nuclear triad is or where various countries are or, you know, the difference between Sunni and Shia in the Muslim world — those are things that he doesn't know and hasn't seemed to spend a lot of time trying to find out about," Obama added.
He agreed Trump is much different than the typical Republican opponent.
"Absolutely. Well for one thing, he doesn't seem to have any plans or policies or proposals or specific solutions," he said. "The good news is we've got a candidate in Hillary Clinton who has put out very specific plans and programs and is telling you exactly what she's going to do."
Obama will address the convention two nights after his wife, Michelle, spoke.
"I'm not going to hit that bar so let me concede top speech-making already to my wife, but I couldn't have been prouder of her," he said. "The way she was able to remind all of us that where this really counts is the kind of message we're sending our kids about who we are and where we want to take this country."
Michelle Obama didn't mention Trump's name but spoke about negative campaigns and bullying.
"She's always been concerned about the tone and the tenor of politics," Obama said. "One of the things that we always talk about with our girls is how do you treat other people."
Obama said Trump is "somebody who likes attention" and that his authoritative style is wrong.
"That's not how our founders designed our system. We're not a government where some strong man orders people around and banishes enemies," he said. "I think that it is important for us to remember that we live in a democracy. And by definition, then, the way we solve problems is by everybody participating and arguing and occasionally having to compromise."
But Trump is winning over voters.
He leads Clinton in the last three national polls: 48-45 percent in the CNN/ORC poll and 44-43 percent in the CBS News poll, both conducted July 22-24, and 47-40 in the LA Times/USC poll conducted July 20-26.
In Nate Silver's latest Electoral College forecast, Trump has a 39.9 percent chance of winning. Clinton is projected to win 286.5 Electoral College votes, 16.5 more than needed to become president.
Trump responded to Obama's comments about him during his news conference in Doral, Fla., saying:
"I think president Obama has been the most ignorant president in our history. His views of the world as he says don't jibe and the world is a mess. He has been a disaster as a president. He will go down as one of the worst presidents in the history of our country. It is a mess. And I believe that Hillary Clinton will be even worse."