US Republican presidential nominee Donald Trump has stirred social media ire by remarking "We have some bad hombres here" and referring to Democratic rival Hillary Clinton as "such a nasty woman".

LISTEN ABOVE: Political commentator Frank Torres, from the Orlando Observer, spoke with Rachel Smalley about the debate

The comments during Wednesday's third and final presidential debate came with Trump struggling to attract support from Latinos and women ahead of the November 8 election.

During the face-off in Las Vegas, Trump repeated his call for tougher security at the Mexican border, saying: "We have to keep the drugs out of our country."

Adding he would also go after major drug dealers in the United States, he said: "We have some bad hombres here and we're going to get them out."

Social media users quickly seized on the remark.

"This #BadHombres is the first of his family to graduate from college, did Americorps & taught in public schools," tweeted Jose N Miranda.

"Sometimes I forget this is a presidential debate and not an SNL (Saturday Night Live) skit #badhombres," wrote Twitter user Ian Mayberry.

The term "Bad Hombres" became one of the most-discussed topics of the night on US social media and was tweeted out about 134,000 times during and immediately after the debate, according to brand intelligence firm Amobee.

Trump has aroused criticism for inflammatory comments about Mexican illegal immigrants during his presidential bid.

During a speech to kick off his campaign in June 2015, Trump accused Mexico of sending rapists and other criminals to the United States.

In late August, Mexican President Enrique Pena Nieto met with the Republican nominee and said later Trump's policies "could represent a huge threat to Mexico".

Later in the debate, Trump interjected as Clinton said she would raise taxes on the wealthy to help fund the US government's Social Security retirement program and that Trump would be paying higher taxes too unless he could get out of it.

"Such a nasty woman," he said.

The comment struck many online as sexist, with over 300,000 tweeting the phrase "nasty woman" by the early hours of Thursday.

"Calling someone a 'nasty woman' on live television is so deeply and unbelievably offensive," tweeted Danielle Suchet.

"'What a nasty woman.' That was the viscerally, awful, genuine part," wrote Jake Swanton.

Trump's campaign was shaken by the recent release of a 2005 tape in which he boasted of kissing and touching women without their consent.