Donald J. Trump insisted on Thursday that he would not cede the right to contest the outcome of the presidential election, even as Democrats and Republicans expressed concern that his position threatened to upend America’s tradition of peaceful power transfers. But in a small gesture of civility, he suggested that he would not dispute the result if the outcome of the race was clear.

Mr. Trump’s reluctance to pledge absolutely that he would honor the election outcome follows a rocky performance in the third and last presidential debate and comes as the candidates set off for the frenzied final stretch of campaigning ahead of the Nov. 8 election. On Thursday, Mr. Trump continued to rally his supporters with conspiracy theories about how the race was rigged against him, but he did make clear that there was one result that he would not challenge under any circumstance.

“I will totally accept the results of this great and historic presidential election — if I win,” Mr. Trump said to cheers at a rally in Delaware, Ohio.

Saying that George W. Bush might have lost the 2000 election to Al Gore if he had made a pre-election pledge not to challenge results, Mr. Trump said he would not take that option off the table. He did, however, try to ease concerns that he was planning to throw the country into postelection turmoil.