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Donald J. Trump has been roiling Republicans by attacking his rivals on their weak poll numbers and questioning their energy (Jeb Bush) and intelligence (Rick Perry).

But the larger threat that he poses to the party is the prospect that he could opt out and run as a third-party candidate. True to form, Mr. Trump is keeping the option open.

In an interview with The Hill newspaper published on Thursday, Mr. Trump said that many of his supporters have been urging him to consider a third-party run if he fails to secure the Republican nomination. Noting that the Republican National Committee has been “foolish” in its handling of him, he said that his treatment by the party will dictate his plans.

“I’ll have to see how I’m being treated by the Republicans,” Mr. Trump said. “Absolutely, if they’re not fair, that would be a factor.”

Some Republicans have questioned whether Mr. Trump is actually a Republican, pointing out that he has donated to Democrats over the years and held liberal positions on issues such as the health care overhaul. But if Mr. Trump runs as a third-party candidate, he could siphon votes away from the 2016 Republican nominee and effectively help a Democrat win the White House.

Many recall how Ralph Nader was accused of being a factor in 2000 when Al Gore lost in a close election to George W. Bush, or in 1992 when H. Ross Perot won nearly 19 percent of the vote nationwide to hurt George Bush and help Bill Clinton prevail.

For his part, Mr. Trump has attributed his Democratic donations as smart business investments and argues that his policy positions have evolved over the years.

The billionaire businessman said last weekend that he thinks it makes the most sense to compete as a Republican but that he is not wedded to it. He also refused to put a limit on how much he would spend on his presidential campaign, saying that if he continues to be performing well in polls he will spend as much as is needed.