The Republican presidential hopeful told the Washington Post he would not step aside, no matter what.
The White House had said Donald Trump was “disqualified” from running after he said the US should ban Muslims from entering the country.
Donald Trump’s comments, in the wake of a deadly terror attack in California, drew global condemnation.
The latest world leader to reject his remarks was Israeli PM Benjamin Netanyahu, who said Israel “respects all religions”, hours after Donald Trump announced he will be visiting the country this month.
Donald Trump is the current frontrunner among the Republicans running for president, six weeks before the primary contests begin for each party to pick their nominee.
He also alluded to running as an independent in a tweet linking to a USA Today poll which found 68% of his supporters would vote for him if he left the Republican Party.
Concerned that Donald Trump could run as an independent, the Republican leaders persuaded the real estate tycoon to pledge to support the eventual nominee.
However, Donald Trump has threatened to leave the Republican Party before if he was not “treated fairly”.
“My whole life is about winning. I don’t lose often. I almost never lose,” he told the Post.
Party officials fear a third-party Trump campaign would split the Republican vote, and give Democrats a winning advantage.
Although Donald Trump has consistently led in national polls for several months, a majority of voters view him unfavorably.
Republican congressman David Jolly has joined a number of commentators who have urged Donald Trump to withdraw from the race.
Donald Trump’s comments about Muslims came after the deadly shootings in San Bernardino, California.
He called for “a total and complete shutdown of Muslims entering the United States until our country’s representatives can figure out what is going on”.
Former Governor of Florida Jeb Bush called Donald Trump “unhinged”. Speaker of the House Paul Ryan said his comments were contrary to American values.
A petition calling for Donald Trump to be barred from entering the UK has gathered more than 250,000 names, so British lawmakers will have to consider debating the issue.
“They don’t know what they’re getting into,” Donald Trump wrote on Twitter about the petition.
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