Mr. Trump, the only one of 10 Republican candidates in a Fox News debate this month who refused to rule out a third-party bid, said that he expected his showing in polls to “go up 10 or 15 percent” if he signs the pledge. He added that if he did sign but lost the nomination, he would not run as an independent, a concern among many Republicans.

“I don’t make commitments and break them,” Mr. Trump said after speaking at an event here hosted by local chambers of commerce. If he violates the contract, he said, “they should sue. I would go before the court and say, ‘I’m guilty.’ ”

Disputing a Huffington Post report that suggested he was assuring local party leaders that he would sign the pledge, he insisted, “I haven’t told anybody that.”