Las Vegas, United States: Donald Trump rides into the last Republican presidential debate of 2015 on Tuesday with his strongest support yet, shaking off intense criticism about his anti-Muslim comments, even as rivals accused him of playing into jihadist hands.

Two polls unveiled Monday and Tuesday show Trump at new heights, with maverick US Senator Ted Cruz surging into second place and looking to rattle the frontrunner on the national stage in Las Vegas.

With just seven weeks before voters in the heartland state of Iowa cast the first ballots in the nominations process, Trump, Cruz and seven other candidates will go toe to toe on CNN beginning at 0130 GMT Wednesday.

Verbal fireworks are expected in the showdown, especially if his top opponents aggressively confront the bombastic real estate tycoon over his call for a ban on Muslims entering the United States.

Ahead of the main event, low-polling rivals Senator Lindsey Graham and 9/11-era New York governor George Pataki slammed Trump in the undercard debate.

"Donald Trump is the know-nothing candidate of the 21st century," boomed Pataki, adding that Trump's proposed Muslim ban "is un-American, it is unconstitutional and it is wrong."

Graham, a hawkish Republican, appeared to extend an olive branch to Muslims, urging Trump and others to "leave the faith alone" and focus on radicals intending to kill Americans.

"Donald Trump has done the one single thing you cannot do: declare war on Islam itself," said Graham, who advocates sending 10,000 US troops to Syria and Iraq to help Arab allies defeat the Islamic State extremist group.

- 'World War III' -

But former senator Rick Santorum, who ran for the White House in 2012, refused to rebuke Trump, saying the billionaire's call for a ban "was nothing against Muslims," but a knock on the administration's inability to properly vet people coming into the United States.

"We have entered World War III," and President Barack Obama refuses to label it America's war against radical Islamic terrorism, Santorum said.

The debate is the first since the deadly attacks in Paris and San Bernardino, California -- violence that has brought national security concerns to the fore and heightened Americans' fears about illegal immigration and Syrian refugees.

Those fears likely played prominently in recent surveys, including a Monmouth University poll released Monday showing 41 percent of Republican voters support Trump, his highest position yet in the poll.

Cruz surged to 14 percent, with 10 percent for Senator Marco Rubio and nine percent for retired neurosurgeon Ben Carson. All others are at three percent or lower.

In an ABC News/Washington Post poll Tuesday, Trump earned 38 percent support among registered Republicans and GOP-leaning independents, a six-point climb from November.

Cruz doubled to 15 percent, while Rubio and Carson were tied at 12 percent each.

Cruz, a first-term senator with huge backing from the ultra-conservative Tea Party movement and evangelical Christians, has emerged as Trump's rival of the moment.

"He's in a pretty good position, especially when you think of evangelical and constitutional conservative types. He's the most viable for them," Seth McKee, associate professor of political science at Texas Tech University, told AFP.

Three of the last five major Iowa polls have Cruz besting Trump, including a Des Moines Register survey that puts the senator from Texas 10 points ahead.

Rubio, also on the rise recently, is polling third in Iowa, followed by Carson, whose slide in the polls is seen by some as a major gain for Cruz.

Jeb Bush, the son and brother of former presidents, is a distant fifth, his campaign spinning its wheels.

Trump exuded confidence Monday night at a Las Vegas rally. 

"I think we're going to win Iowa, I think we're going to win New Hampshire big," he said. "If we win Iowa, we run the table."

Establishment candidates like Bush, New Jersey Governor Chris Christie and Ohio Governor John Kasich are expected to lash out against Trump in the prime-time debate, which also features business executive Carly Fiorina and Senator Rand Paul.

"This will not be like an evening in paradise for me," Trump admitted.

Cruz, while eager to draw a distinction between himself and Trump, may be careful not to antagonize him, according to experts.

"If he needs to fight back, he will. But that's not his style," McKee said.

"He might push back with a smile on his face."

Rubio could take a swing at Cruz. Foreign policy and national security are widely regarded as Rubio's wheelhouse, and on Sunday he accused Cruz of being "isolationist" and for opposing bulk phone data collection.