Republican presidential frontrunner Donald Trump grabbed a big win in the South Carolina primary on Saturday, while Democrat Hillary Clinton breathed life into her sluggish campaign with a victory over Bernie Sanders in Nevada.

The wins for the brash billionaire and the former secretary of state give the candidates a major boost heading into the next major phase of the White House race -- Super Tuesday on March 1, when about a dozen states go to the polls.

But the rough-and-tumble campaign claimed another victim when former Florida governor Jeb Bush -- brother and son to two US presidents -- dropped out of the race after another poor showing. 

In South Carolina, the 69-year-old Trump triumphed, capturing about a third of the votes, with about 87 percent of the precincts reporting. 

His supporters erupted in a roar when CNN called the contest in his favor -- his second win of the nominations race after New Hampshire and an important test of the strength of his bid to succeed President Barack Obama. 

"There is nothing easy about running for president, I can tell you," Trump told his victory party in Spartanburg. "It's tough, it's nasty. It's mean. It's vicious. It's beautiful."

"When you win, it's beautiful," he added to cheers.

After several nail-biting hours, final results showed that the second place in the Palmetto State went to Florida Senator Marco Rubio.

Rubio eked out a narrow 22.5 percent victory over Texas Senator Ted Cruz, who had 22.3 percent of the vote.

Both are Cuban-American first-time senators.

"After tonight, this has become a three-person race and we will win the nomination," a confident Rubio proclaimed.

In Nevada, Clinton claimed a major win. With about 88 percent of precincts reporting, Clinton was at 52.6 percent to 47.4 percent for Sanders.

"This is your campaign, and it is a campaign to break down every barrier that holds you back," Clinton said in her victory speech at her Caesars Palace headquarters on the Las Vegas Strip.

 'Take a risk' with Trump

 In South Carolina, Trump -- a onetime reality TV star who has upended the political landscape with his take-no-prisoners style and tough talk on everything from Muslims to Mexico to waterboarding -- showed he could compete for the long haul. 

"We just think we want to take a risk with Trump. We think he's had success with everything he's touched," Lynn Derrick, a first-time primary voter, told AFP at a high school in the state capital Columbia.

Trump and Cruz, who won the Iowa caucuses, duked it out in the week leading up to Saturday's primary, with the campaign growing increasingly nasty. 

Trump ended up in a spat with Pope Francis, who hinted the tycoon was "not a Christian" for wanting to build a wall on the border with Mexico. He also called for a boycott of Apple over its refusal to unlock the phone of a suspect in the San Bernardino attacks.

The results were not good news for Bush, Ohio Governor John Kasich and retired neurosurgeon Ben Carson, who were relegated to the second tier of candidates.

Bush did not wait long to throw in the towel.

"In this campaign, I have stood my ground, refusing to bend to the political winds," he said.

 Clinton wins in desert

 In the desert state of Nevada, the 68-year-old Clinton scored a major win, but Sanders proved he was in it for the long haul.

"Some may have doubted us, but we never doubted each other," Clinton said in a fiery left-leaning speech, clearly aimed at the minority voters who make up roughly half of the state's population -- and who are key in the American South.

Clinton claims that Sanders is offering impractical, pie-in-the-sky ideas that he cannot bring to fruition as president, and on Saturday took aim at corporate America -- usually a message sounded by Sanders.

"If you cheat your employees, exploit consumers, pollute our environment, or rip off taxpayers, we're going to hold you accountable," the former secretary of state said.

"But if you do the right things, if you invest in your workers, contribute to your communities, help build a better America -- we're going to stand with you."

Clinton, who won by a hair in Iowa but was crushed by Sanders in New Hampshire, had counted on a major Hispanic voter turnout, especially among Las Vegas hotel and casino employees. 

But according to CNN entrance polls, while she handily won the black vote, the Latino vote was more evenly split -- evidence that the Sanders campaign may have much longer legs than first expected.

Clinton did well with women, but was stomped once again by Sanders with young voters, the polls showed.

Sanders congratulated Clinton, but also said he was proud of having significantly narrowed the gap.

"We have the wind at our back as we head toward Super Tuesday," the 74-year-old Sanders said, looking ahead to the showdown, when about a fifth of the Democratic nominating delegates are up for grabs.