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The Republican National Committee is pushing back against Donald J. Trump’s claim that the jeers that serenaded him during the presidential debate on Saturday were from an audience stacked with big money donors.

Mr. Trump made the claim on the debate stage as his responses were met with loud boos. He reiterated on Monday in South Carolina that the party was working against him.

“When I walked in it was like my wife was clapping, my kids were clapping, but the whole room was made up of special interests and donors, which is a disgrace from the R.N.C.,” Mr. Trump said.

Sean Spicer, a spokesman for the commitee, offered a breakdown of debate attendance on Saturday night to show the relatively small number of donors in the audience. Of the approximately 1,600 people who attended, 300 tickets were given to Republican “grass-roots” activists and elected officials, 600 were divided evenly among the six candidates, and only 10 went to R.N.C. donors.

The remaining tickets, according to Mr. Spicer, went to the South Carolina Republican Party and to CBS, which hosted the debate.

A senior official with the South Carolina Republican Party estimated that there were no more than 300 donors in the crowd.

Discrediting his detractors is not a new approach for Mr. Trump. When he faced an unfriendly audience in New Hampshire last week, he suggested that the national committee was trying to keep his supporters away.

“Let me just tell you, we needed tickets,” Mr. Trump said. “You can’t get them. You know who has the tickets — to the television audience? Donors, special interests, the people that are putting up the money. That’s who it is. The R.N.C. told us.”

With the rift between Mr. Trump and the Republican Party widening, he re-issued his threat to walk away from a pledge that he made last year to support the eventual nominee and not embark on a third-party run.

“I signed a pledge, but it’s a double-edged pledge,” Mr. Trumps said. “And as far as I’m concerned, they’re in default of their pledge.”