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

The victories by Trump and Clinton solidified their positions as the front-runners to win their parties' respective presidential nominations ahead of the Nov. 8 election.

Former Florida Governor Jeb Bush suffered a distant-fourth-place finish 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," an emotional Bush said in Columbia. He finished far out of the running in each of the first three states.

Trump won 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.

Trump, 69, 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 percent of South Carolina precincts reporting, Trump had 33.9 percent, followed by Cruz with 21.8 percent and Rubio with 21.5 percent.

"People (pundits) gave me no chance in South Carolina. Now it looks like a possible win. I would be happy with a one vote victory! (HOPE), (sic)" Trump tweeted shortly before the television networks declared him the winner.

It was Trump's second victory in a row, after New Hampshire Feb. 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 midwestern and northern states in the state-by-state contest to pick nominees for the Nov. 8 election.

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

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

With 85 percent of precincts reporting, Clinton was leading with 52.5 percent of the vote to Sanders' 47.4 percent. Vote counting was delayed in Nevada by heavy turnout.

Clinton's victory buoyed worried supporters and gave her fresh momentum as she heads into the next contest in South Carolina Feb. 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."

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," he said. "We have the momentum."

After routing Clinton in New Hampshire and finishing a strong second in Iowa, states with nearly all-white populations, Sanders had hoped to prove in Nevada 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 percent to 22 percent, a bad omen for South Carolina and other southern states with big black populations. He did win among Hispanics by 53 percent to 45 percent.

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 Clinton and have been slow to warm to Sanders.

Trump, the bellicose New York billionaire, created some last-minute drama in South Carolina after Pope Francis said Thursday his views on US immigration were "not Christian." Trump initially called Francis "disgraceful," but later called him "a wonderful guy."

The Vatican later clarified the pope's remarks, saying they were "in no way" a personal attack and were not an indication how to vote.

Trump stirred fresh controversy Friday when he told a crowd about a US general who was said to have dipped bullets in pigs' blood to kill Muslim prisoners a century ago.