Republican presidential candidate Marco Rubio has received boosts in his drive to become the mainstream Republican alternative to frontrunner Donald Trump, with a string of high-profile endorsements and missteps by rival Ted Cruz's campaign.

Rubio, who eked out a second-place finish in South Carolina's primary by fewer than 1000 votes over Cruz on Sunday, racked up endorsements from prominent Republicans including US Senator Orrin Hatch of Utah, Arkansas Governor Asa Hutchinson and former presidential candidate Bob Dole.

Rubio and Cruz came out of South Carolina with sharper criticism of Trump, who swept the Southern state with a comfortable margin of victory. At the same time, the two senators' rivalry intensified - and soured.

Cruz fired his main spokesman, Rick Tyler, over a video that falsely showed Rubio dismissing the Bible.

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Tyler had apologised for posting "an inaccurate story" involving a video purporting to show Rubio referring to the Bible and saying, "Not many answers in it". Tyler had retweeted a link to the misleading video and posted it on Facebook.

Cruz fired Tyler the next day, saying his campaign did not question the faith of other candidates. "That's why I'm asking for Rick Tyler's resignation," Cruz said.

The first-term senators from Texas and Florida are locked in a battle to become their party's alternative to political outsider Trump in Nevada's caucus today, the last Republican presidential contest before the busy voting month of March.

Tyler's dismissal came amid intense criticism of the Cruz campaign as dishonest from both Rubio and Trump.

Rubio spokesman Alex Conant called Cruz a "candidate willing to do or say anything to get elected". "There is a culture in the Cruz campaign, from top to bottom, that no lie is too big and no trick too dirty," he said.

Trump seized the opportunity to pile on Cruz, whom he has repeatedly characterised as a liar."Ted Cruz has now apologised to Marco Rubio and Ben Carson for fraud and dirty tricks. No wonder he has lost Evangelical support!," said Trump, who has derided Cruz for failing to live up to expectations he would get solid support from evangelical Christians in South Carolina.

Opinion polls show Rubio and Cruz running close in Nevada, and both candidates hope to get a boost going into the contests in a dozen states on March 2.

Cruz fired his main spokesman, Rick Tyler, over a video that falsely showed Rubio dismissing the Bible. Photo / AP
Cruz fired his main spokesman, Rick Tyler, over a video that falsely showed Rubio dismissing the Bible. Photo / AP

Trump is ahead in threequarters of the next states. Latest polls showed the billionaire with seemingly insurmountable margins in Massachusetts, Alabama and Vermont, with narrower advantages in Virginia, Georgia, Tennessee, Oklahoma and Alaska. Cruz held a narrow lead in his home state, and in Arkansas, while Rubio was up by two points in Minnesota.

Larry Sabato, director of the University of Virginia Centre for Politics, said: "If someone is going to beat Trump then Rubio probably has the best shot but the hour is growing late. He can't keep on finishing second or third. You have to start winning, but where?"

Meanwhile, Ohio Governor and candidate John Kasich has been accused of old-fashioned sexism. Describing his first successful election campaign in the 1970s, he told a meeting in Virginia: "We just got an army of people and many women who left their kitchens to go out and go door to door and to put yard signs up for me."

His campaign staff insisted that Kasich was describing social conditions at the time. The comment was lampooned mercilessly on Twitter - where some pointed out that it coincided with him signing into law on Monday a bill banning the use of Ohio state funds to any agency that promotes or performs abortions.

- Telegraph Group Ltd, AAP