Hillary Clinton and Donald Trump have clashed over the rights of women to have abortions as the candidates locked horns in Las Vegas in the final US presidential debate.

The two candidates did not shake hands as they entered the stage at the University of Nevada for their third election clash.

Mr Trump said he planned to appoint "pro-life judges" to the Supreme Court and allow individual states to determine whether to allow abortion.

The Republican nominee said: "If you go with what Hillary is saying you can take the baby and rip the baby out of the womb of the mother just prior to the birth of the baby.

"You can can say that's OK, and Hillary can say that's OK, but that's not OK with me.

"Based on what she's saying ... you can take the baby and rip the baby out of the womb in the ninth month, on the final day, and that's unacceptable."

Mrs Clinton responded: "That's not what happens in these cases and just using that kind of scare rhetoric is just terribly unfortunate."

"This is one of the worst possible choices that any woman and her family has to make and I do not believe the government should be making it," Clinton said.

Clinton vowed to appoint justices who would uphold the ruling legalizing abortion.

Both Republican and Democratic candidates said they supported the second amendment - the right to bear arms - in a discussion on gun control.

Fox News host Chris Wallace is moderating the third election clash, which covers six topics - debt and entitlements, immigration, economy, the Supreme Court, foreign hotspots and fitness to be president.

Mr Trump is facing a battle to win over undecided voters ahead of the November 8 election, with multiple polls showing Democrat Mrs Clinton is leading the race to the White House.

US president Barack Obama's half brother Malik was in the debate audience as a guest of Mr Trump, after he told the New York Post the Republican "can make America great again".

Hours before the debate, several taco vans lined up outside the Trump Hotel near the Las Vegas Strip in a protest over the Republican candidate.