“I see no circumstances under which I would tear up that pledge,” he said in a news conference at Trump Towers in New York City.
Mr Trump made the announcement following a meeting with Republican National Committee chairman Reince Priebus.
The party has asked its pool of 17 candidates to sign a non-legally binding loyalty pledge to ensure future party unity, which analysts say was aimed directly at Mr Trump.
The real estate baron was booed in a televised debate last month when he refused to rule out a third-party campaign if Republicans didn’t pick him as theirWhite House candidate.
The pledge states: “I, _________, 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.”
Party chiefs fear an independent campaign by Mr Trump could suck votes away from the eventual Republican nominee, thereby handing victory to the Democratic candidate, which many strategists expect to be Hillary Clinton.
Ross Perot’s third party bid in 1992 is sometimes said to have cost George H W Bush a second term in the White House and allowed Bill Clinton to win.
However, polls back then showed Perot supporters were split right down the middle in their second choice between Mr Bush and Mr Clinton.