Republican presidential candidates Marco Rubio and Ted Cruz are locked in a battle to become their party's alternative to New York billionaire Donald Trump in Nevada's Tuesday caucus, the last presidential contest before the busy voting month of March.

Opinion polls show the two U.S. senators running close in the western state after a Saturday primary in South Carolina where Rubio bested Cruz by fewer than 1,000 votes, Trump swept the state by 10 percentage points and one-time favorite Jeb Bush dropped out.

Both Rubio and Cruz came out of South Carolina with sharper criticism of Trump and an eye to the 12 Super Tuesday races on March 1. That date is the crown jewel in the state-by-state nominating contests to pick the Republican and Democratic candidates who will face off in the Nov. 8 presidential election.

Rubio assailed the former reality TV star's credentials on foreign policy and healthcare, while Cruz hammered at what he called Trump's liberal views on abortion and health policy.

Trump, more magnanimous toward his rivals the day after his latest victory, returned to his trademark combative style on Monday morning with a string of insults on Twitter.

Announcing his arrival at Trump International Hotel in Las Vegas, Nevada, Trump derided Cruz for failing to live up to expectations he would enjoy the solid support of evangelical Christians in South Carolina. "The reason that Ted Cruz lost the Evangelicals in S.C. is because he is a world class LIAR, and Evangelicals do not like liars!" Trump exclaimed.

"Rubio and Cruz were pummeled. So glad Jeb is gone! Next no liar!" Trump posted. He also targeted Rubio, saying he did not fulfill promises to voters in his home state of Florida.

Ohio Governor John Kasich kept his focus on bigger states including Michigan and Virginia, where he was campaigning on Monday, hoping to garner enough support there among mainstream Republicans.

Kasich, endorsed by The New York Times and given a boost by his No. 2 finish to Trump in New Hampshire, got the backing on Sunday of Stanley Druckenmillion, a hedge fund billionaire.

Democratic candidates Hillary Clinton and U.S. Senator Bernie Sanders of Vermont were also looking south. Sanders, who is campaigning in Virginia on Monday, could face an uphill battle to recover from his loss to Clinton in the party's Nevada caucuses on Saturday.

Their next contest is on Saturday in South Carolina, quickly followed by the Super Tuesday races that include a number of southern states with large Hispanic and African American populations.