US election: Donald Trump, Hillary Clinton take South Carolina, Nevada caucuses; Jeb Bush suspends campaign

Republican Donald Trump has rolled to victory in South Carolina and Democratic presidential candidate Hillary Clinton beat back a strong challenge from Bernie Sanders in the Nevada caucuses.

Former Florida governor Jeb Bush suffered a distant fourth place finish in the Republican race and announced he had suspended his campaign, ending his dream of becoming a third Bush president after his father and brother.

"The people of Iowa, New Hampshire and South Carolina have spoken, and I really respect their decision," Mr Bush said in Columbia.

He finished far out of the running in each of the first three states.

Mr Trump won South Carolina despite getting into a controversy with Pope Francis and having a debate performance that raised questions about his temperament in the days before the voting.

He easily defeated Florida senator Marco Rubio and Texas senator Ted Cruz, who were in a close fight for second place and the right to declare themselves the main anti-Trump alternative.

With 57 per cent of South Carolina precincts reporting, Mr Trump had 33.9 per cent, followed by Mr Cruz with 21.8 per cent and Mr Rubio with 21.5 per cent.

"People [pundits] gave me no chance in South Carolina. Now it looks like a possible win," Mr Trump tweeted shortly before the television networks declared him the winner.

"I would be happy with a one vote victory! (HOPE)."

It was Mr Trump's second victory in a row, after New Hampshire on February 9, an outcome that frightens establishment Republicans but thrills the "throw-the-bums-out" conservative base of the party that has long been fed up with Washington.

After South Carolina, the Republican presidential campaign is about to rapidly pick up steam in March when dozens of states hold nominating contests.

Another candidate, Ohio Governor John Kasich, is concentrating on mid-western and northern states in the state-by-state contest to pick nominees for the November 8 election.

Clinton's victory buoyed worried supporters

Mrs Clinton's victory in the Nevada Democratic caucuses could help calm Democratic Party worries about the strength of her campaign.

Her win denied Mr Sanders the breakthrough win he sought in a state with a heavy minority population but his ability to close a one-time double-digit polling lead for Mrs Clinton suggested the Democratic nominating race could be long and hard fought.

With 85 per cent of precincts reporting, Mrs Clinton was leading with 52.5 per cent of the vote to Sanders' 47.4 per cent.

Vote counting was delayed in Nevada by heavy turnout.

Mrs Clinton's victory buoyed worried supporters and gave her fresh momentum as she heads into the next contest in South Carolina on February 27, where polls show her with a double-digit lead largely as a result of heavy support from black voters.

"Some may have doubted us, but we never doubted each other," she told cheering supporters at a victory rally in Las Vegas.

"This is your campaign."

We have the momentum: Sanders

Mr Sanders vowed to fight on and set his sights on the 11 states that vote on "Super Tuesday," March 1.

He predicted that when Democrats gather for their nominating convention in Philadelphia in July: "We are going to see the results of one of the great political upsets in the history of the United States."

"The wind is at our banks," Mr Sanders said.

"We have the momentum."

After routing Mrs Clinton in New Hampshire and finishing a strong second in Iowa, states with nearly all-white populations, Mr Sanders had hoped to prove in Nevada that he could win over black and Hispanic voters and compete nationally as the race moves to states with more diverse populations.

But entrance polling in Nevada showed he badly lost among black voters, by 76 per cent to 22 per cent, a bad omen for South Carolina and other southern states with big black populations.

He did win among Hispanics by 53 per cent to 45 per cent.

Mrs Clinton's campaign has argued she would assert control of the Democratic race once it moved to more diverse states with black and Hispanic populations, who have traditionally backed Mrs Clinton and have been slow to warm to Mr Sanders.