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The pledge is aimed at Trump, the current Republican front-runner, who has multiple times threatened to run as a third-party candidate in the event Republicans do not treat him "fairly" and attempt to push him out of the race.
The pledge was confirmed by at least one candidate's campaign and reported in multiple outlets. The text of the proposed pledge, according to Politico, reads:
"I [name] affirm that if I do not win the 2016 Republican nomination for president of the United States I will endorse the 2016 Republican presidential nominee regardless of who it is. I further pledge that I will not seek to run as an independent or write-in candidate nor will I seek or accept the nomination for president of any other party."
Trump will meet on Thursday with Republican National Committee Chair Reince Priebus, an RNC official told Business Insider.
Trump's campaign said late Wednesday that he will host a news conference at Trump Tower in New York on Thursday at 2 p.m. ET, when he could address the pledge. Trump's campaign didn't elaborate on any further details about the press conference. The Trump campaign did not respond to a request for comment.
The relationship between Trump and the RNC has been complicated since the real-estate mogul entered the race in mid-June. He has drawn intense scrutiny over his comments on immigration, his remark on Sen. John McCain's (R-Arizona) war record, and his feud with Fox News host Megyn Kelly.
Trump has said he wants to run as a Republican but has been dangling the third-party threat as "leverage." The first Republican presidential debate last month began with fireworks when the candidates were asked by Fox News moderator Bret Baier if they would vow to support the eventual GOP nominee and "pledge to not run an independent campaign against that person."
Only Trump raised his hand and said he couldn't make that commitment.
"I cannot say I have to respect the person that - if it's not me - the person that wins," Trump said.
"If I do win, and I'm leading by quite a bit, that's what I want to do. I can totally make that pledge: If I'm the nominee, I will pledge that I will not run as an independent," Trump said, adding, "And I am discussing it with everybody. I'm talking about a lot of leverage. We want to win and we will win. But I want to win as the Republican. I want to run as the Republican nominee."
REUTERS/Brian Snyder Republican 2016 U.S. presidential candidate businessman Donald Trump (L) talks with fellow candidate and former Governor of Florida Jeb Bush during a commercial break at the first official Republican presidential candidates debate of the 2016 U.S. presidential campaign in Cleveland, Ohio, August 6, 2015. 
The move by the Republican National Committee comes as GOP candidates are increasingly questioning Trump's party loyalty. Former Florida Gov. Jeb Bush (R), for example, has unleashed multiple attacks in recent days highlighting Trump's past deviations from traditional Republican Party positions.
It's not clear what the RNC would do if Trump refused to sign the pledge. Conservative pundit George Will suggested last month that party leaders could stipulate that future debates should only be open to candidates who "pledge to support the party's nominee."
At least one key early-voting state's Republican Party has moved to force Trump to make a decision soon. To get on the South Carolina primary ballot, Republican candidates must sign a filing form that includes a pledge to "affirm that I generally believe in and intend to support the nominees and platform of the Republican Party in the November 8, 2016 general election."
For his part, last weekend, Trump said he would decide "soon" on a third-party run.