donald trump.jpg
Photograph: Photo by Gage Skidmore, used under CC BY-SA

Billionaire businessman Donald Trump won the Republican primary in the southern US state of South Carolina Saturday, vowing to pick up momentum as the field of candidates narrowed with former Florida governor Jeb Bush quitting the race.

Trump had 32.6 per cent of the vote, state election officials said. His closest rivals Florida Senator Marco Rubio and Texas Senator Ted Cruz battled for second place, with 22.5 per cent and 22.1 per cent of the vote respectively.

The results give Trump momentum heading into the next contest in Nevada on Tuesday, and the Super Tuesday primary on March 1 when more than a dozen states hold primaries.

Meanwhile, former secretary of state Hillary Rodham Clinton beat Vermont Senator Bernie Sanders in a separate Democratic caucus in the western state of Nevada.

Trump told supporters that he anticipates big victories ahead.

"Let's have a big win in Nevada," he said. "Let's have a big win in the [March 1 primaries]. Let's put this thing away and let's make America great again."

Trump supporters had expressed anger at a broken political system and the influence of big campaign donors in politics.

Trump "can't be bought and he'll tell you to your face what he thinks and how he feels," Michael Reilly, 18, told dpa as he voted for the first time.

The candidates trailing Trump hope to emerge as the alternative to the real estate tycoon, whose brash campaign style has equally alienated and energized Republican voters. The first two contests in Iowa and New Hampshire saw wins for Cruz and Trump, respectively.

But Trump dismissed pundits who say as that as the Republican field narrows, the anti-Trump vote will consolidate.

"What they don't understand is that as people drop out, I'm going to get those votes too," he said.

Jeb Bush, the son and brother of former US presidents, ended his quest to be the Republican nominee for president after failing to make a strong showing in South Carolina and the two previous states to vote.

Announcing his decision to supporters, the former Florida governor said he's had a "front row seat" to the US presidency and anyone assuming that office must know he or she is "a servant, not a master."

The next president must serve with "honour and decency" said Bush, who had taken on Trump over his divisive rhetoric and profane language.

Both Rubio and Cruz sought to cast their results as providing momentum to their campaigns moving forward.

"Now, practically speaking, it's down to three," Rubio said. "And I know that our campaign gives us the best chance not just to come together, not just to unify our party but to unify our country and to grow this movement."

Cruz insisted that he was the only candidate who had beaten Trump in Iowa and could beat him again in the future.

In Nevada, with 88 per cent of the ballots counted, Clinton had won 52.6 per cent of the vote to 47.3 per cent for Sanders.

"Some may have doubted us, but we never doubted each other," Clinton said in a victory speech.

Saying her campaign was about building "ladders of opportunity," Clinton took a subtle dig at her opponent by noting that the US was not "a single-issue country."

Sanders's campaign has focused sharply on economic inequality and the power of large financial institutions.

Sanders congratulated Clinton and praised his supporters for making the race close after being so far down in the polls only weeks before.

Clinton had once held a substantial lead bolstered by the western state's large Hispanic population, but saw her advantage slip after Sanders notched a large victory in New Hampshire and ended in a near tie in Iowa.

The Clinton campaign had stressed she was better positioned to gain support of the minority voters who are a key Democratic voting bloc in Nevada.

Her campaign had described Nevada, South Carolina and southern states with primaries next month as her "firewall" on the path to the nomination, as Sanders, a self-described democratic socialist, has seen his message of economic equality resonate with voters.

The Democrats next hold their own primaries in South Carolina on February 27 and Republican hold caucuses in Nevada on Tuesday.

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