Donald Trump has been warned by the head of the Republican National Committee to tone down his comments on immigration that have incensed and alienated an election constituency.

Republican Chairman Reince Priebus has underscored the concerns of party leaders that Trump could be giving the Republican Party a bad image with his comments in particular of Mexico and Mexican nationals, according to The Washington Post.

Billionaire Trump, who has his own reality TV show, has been known to thrive on controversy and attention, which may make him difficult to control.

Given the chance to apologize on NBC News, Trump did not back down from his comments and retained his views on illegal immigrants as "rapists and killers, among other things," NBC News reported.

He told NBC News that he has "nothing to apologize for" in his repeated remarks about Mexicans.

Trump noted that he would build an "impenetrable" wall between the U.S. and Mexico and that he would "make" the Mexican government pay for it.

The billionaire was also confident that he will secure the Latino vote if the GOP selects him as the presidential candidate and standard-bearer.