Republican nominee Donald Trump said Thursday that he will accept the result of the presidential race on Nov. 8 — if he defeats Democrat Hillary Clinton.

Otherwise, Mr. Trump said, he is keeping his options open until he is convinced that Election Day shenanigans will not poison the outcome.

“Ladies and gentlemen, I want to make a major announcement today,” Mr. Trump said at a rally in Delaware, Ohio. “I would like to promise and pledge to all of my voters and supporters and to all of the people of the United States that I will totally accept the results of this great and historic presidential election — if I win.”

President Obama, campaigning on behalf of Mrs. Clinton, took issue with Mr. Trump’s remarks and claims of a “rigged” election process. He said they are “no joking matter.”

“If you’ve noticed, the Donald is already whining that the vote is going to be rigged before the game is even over,” Mr. Obama told a crowd in Miami. “He is already like, ‘Oh, the game is rigged’ — except today, of course, he said it is not rigged if I win.”

In his third and final debate with Mrs. Clinton on Wednesday night, moderator Chris Wallace of Fox News pressed Mr. Trump about whether he would respect the final vote tally.

“What I’m saying is that I will tell you at the time,” Mr. Trump said. “I’ll keep you in suspense. OK?”

The response put Mr. Trump at odds with his running mate, Indiana Gov. Mike Pence, and members of his campaign team. They also dominated much of the news coverage from a debate that was widely viewed as one of the Republican candidate’s last best chances to change the trajectory of a race that polling suggests is slipping away from him.

Trump supporters, though, said previous White House hopefuls have reserved the right to challenge election results and that Mr. Trump’s comments were consistent with his concerns that widespread voter fraud could boost Mrs. Clinton.

Mr. Obama, meanwhile, said Mr. Trump is trying to save face because he is losing.

“That is dangerous,” he said. “Because when you try to sow the seeds of doubt in people’s minds about the legitimacy of our elections, that undermines our democracy.”

First lady Michelle Obama also piled on the criticism while campaigning for Mrs. Clinton in Arizona, which appears to be up for grabs despite having voted for the Democratic presidential candidate just once since 1950.

“You do not keep American democracy in suspense,” Mrs. Obama said. “Too many people have marched and protested and fought and died for this democracy.”

In Ohio, Mr. Trump stood his ground, demanding “fairness in the election.”

“This is having nothing to do with me. But having to do with the future of our country,” he said.

Mr. Trump told supporters that it would be premature to sign off on the election results 18 days out when Mrs. Clinton has displayed that she cannot be trusted and will do anything to win.

“Hillary Clinton is the most corrupt and dishonest person even to seek the office of the presidency,” he said.

Mr. Trump said he will keep his options open much like Democrat Al Gore did in 2000 when he sought to challenge the results in Florida, which delivered the White House to Republican George W. Bush.

“Of course I would accept a clear election result, but I would also reserve my right to contest or file a legal challenge in the case of a questionable result, and always I will follow and abide by all of the rules and traditions of all of the many candidates who have come before me — always,” he said.

A Suffolk University poll released Thursday showed Mr. Trump and Mrs. Clinton tied in Ohio. The same poll last month showed Mr. Trump with a 3-percentage-point edge.

“The race couldn’t get any closer in the Buckeye State,” said David Paleologos, director of the Suffolk University Research Center in Boston. “Hillary Clinton has closed the narrow gap with Donald Trump since September, and the final outcome in Ohio could come down to the energy of each candidate’s base and the respective campaigns’ get-out-the-vote operations.”

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