The US senator from Texas, who won the Iowa caucuses last week and placed third yesterday night in New Hampshire, wasted no time slinging mud against Trump as a fake conservative, as Cruz fights to be the evangelical and right-wing standard bearer for the 2016 Republican nomination.

Cruz highlighted the 'significant glaring differences' between the two on health care, stressing that Trump was keen on ''adopting Bernie Sanders-style socialized medicine," a reference to the independent senator challenging Hillary Clinton for the Democratic nomination.

Trump and Cruz both say they want to dismantle President Barack Obama's Affordable Care Act, but Trump has been hammered by conservative rivals for expressing support years ago for universal health care.

The pair occupy the far-right lane in the crowded Republican nomination race, with a handful of more mainstream candidates -- Senator Marco Rubio, former Florida governor Jeb Bush, and Ohio Governor John Kasich who finished second in New Hampshire -- seeking to push them aside.

Trump leads in South Carolina with 36 percent support in the RealClearPolitics poll average. Cruz runs second at 20 percent, with Rubio well back in third, below 13 percent.

With Trump proving in New Hampshire that he can win over a broad coalition of Republicans and independent voters, and Cruz riding high among evangelicals and other social conservatives, the Trump-Cruz battle will be paramount, with mainstream candidates likely scrapping for bronze in South Carolina.

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