This story has been updated.

The Republican National Committee, in a move designed to box in Donald Trump and prevent him from a third-party run, on Wednesday asked the party's presidential candidates to sign a loyalty statement vowing not to run as an independent or third-party candidate in the general election.

Trump and RNC Chairman Reince Priebus plan to meet Thursday in New York, according to a Trump campaign spokeswoman. Trump has scheduled a 2 p.m. news conference where he could make an announcement about the RNC pledge.

All summer, Republican leaders have been trying to prevent Trump, the billionaire businessman who has rocketed to the top of GOP polls, from running as an independent candidate if he does not win the Republican nomination. In the Aug. 6 debate, Trump memorably refused to rule out a third-party run -- though he has since signaled a possible change of heart as some state parties are requiring loyalty oaths as a condition of appearing on their state's primary ballots.

RNC staffers reached out to campaigns requesting that their candidates sign a document pledging loyalty to the party's eventual nominee, according to campaign officials.

"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," reads the document. "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."

The pledge was first reported Wednesday afternoon by Politico, while Trump's meeting with Priebus was first reported by The New York Times.

Former RNC chairman Jim Gilmore, who is one of 17 GOP presidential candidates, said he supports the national party's push for candidates to pledge loyalty.

"If someone is going to go to the party and ask for their support, if they’re going to ask the rank and file for their vote, that comes with an obligation for loyalty, in my mind," said Gilmore, a former Virginia governor. "Generally speaking, if you want the party’s support, that loyalty should be there."

Speaking in New Hampshire late Wednesday, Ohio Gov. John Kasich (R) said he would sign the pledge. Scott Milburn, a Kasich adviser, confirmed that the campaign has received the document.

Michael Steele, another former RNC chairman, said Priebus had wanted to get Trump's flirtation with a third-party run "cleared up" before the next debate, scheduled for Sept. 16 on CNN.

"I appreciate what he is trying to do, trying to bring some level of order to this situation," Steele said. "The expectation should be if you’re running to be nominee of the party, you should support the nominee of the party."

Steele added that Trump may have calculated that "there is no real upside to poking the party in the eye. He doesn't want people to peel off from him because they don’t see him as being a team player. I think that’s the way he sees it."