Ted Cruz
Ted CruzReuters

U.S. Republican presidential candidate Ted Cruz won Saturday nominating contests in Kansas and Maine, staking his claim to be the prime alternative for Republicans bent on stopping front-runner Donald Trump.

Trump won one state and led in partial results in another, taking another step toward the Republican nomination in the November 8 presidential election on a night when five U.S. states voted in nominating contests.

It was a bad night for the other Republican candidates, with U.S. Senator Marco Rubio from Florida and Ohio Governor John Kasich shut out in four Republican contests, falling behind Cruz in the battle to become the leader of the party's anti-Trump forces.

Next up will be a crucial contest on Tuesday in the big industrial state of Michigan. Republicans in three other states — Mississippi, Idaho and Hawaii — also will vote Tuesday.

On the Democratic side, front-runner Hillary Clinton won in Louisiana, and her rival Bernie Sanders, a U.S. senator from Vermont, won in Kansas and Nebraska in results that will not substantially change Clinton's big lead in delegates.

Cruz, a first-term U.S. senator from Texas who has promoted himself as more of a true conservative than Trump, also won a non-binding "straw poll" of activists earlier in the day at the Conservative Political Action Conference near Washington, D.C.

"The scream you hear, the howl that comes from Washington, D.C., is utter terror at what 'We the People' are doing together," Cruz told supporters in Coeur d'Alene, Idaho, after his early win in Kansas.

Cruz, 45, has run as an outsider bent on shaking up the Republican establishment in Washington. A favourite of evangelicals, he has called for the United States to "carpet bomb" the Islamic State militant group and has pledged to eliminate the tax-collecting Internal Revenue Service and four cabinet agencies and to enact a balanced budget amendment.

"What we're seeing is the public coming together, libertarians coming together, men and women who love the Constitution coming together and uniting and standing as one behind this campaign," Cruz said in Idaho.

Trump still has a substantial lead in the delegates needed to secure the nomination at the Republican National Convention, but since winning seven of 11 contests on Super Tuesday he has come under withering fire from a Republican establishment worried he will lead the party to defeat in November's election.

Mainstream Republicans have blanched at Trump's calls to build a wall on the border with Mexico, round up and deport 11 million undocumented immigrants and temporarily bar all Muslims from entering the United States.

Saturday's four Republican contests together account for just 155 delegates. The results in Maine gave Cruz 12 delegates and Trump nine. In Kansas, Cruz picked up 24 delegates while Trump gained nine.

The races Saturday were open only to registered Republicans, excluding the independent and disaffected Democratic voters who have helped Trump's surge to the lead.

Saturday's contests were the first since retired neurosurgeon Ben Carson dropped from the race, after polling in the single-digits in most of the nominating contests. Carson had drawn support from evangelical voters, a group that has also been a stronghold of Cruz.

At Saturday's Conservative Political Action Conference, Rubio criticised the media for fuelling Trump's rise.

"I've been sitting here for five minutes and two of the three questions you've asked have been about Donald Trump," Rubio said during a question-and-answer session.

Rubio, a frequent target of Trump's attacks, also said he "didn't get into this race to beat up on other candidates." But, he added, "If someone keeps punching people in the face, eventually someone's going to have to stand up and punch him back."

At a rally in Rubio's home state Saturday, Trump criticised his opponent using a favourite nickname — "little Marco."

"He's a nasty guy, said nasty things, and you know? We hit him hard. Little nasty guy," Trump told the cheering crowd.

The anti-Trump forces have a short window to stop the caustic businessman, who, ahead of Saturday had accumulated 319 of the 1,237 delegates needed to win the nomination at July's Republican national convention, outpacing Cruz, who had 226 delegates.

The delegate-rich states of Florida, Illinois, Ohio, Missouri and North Carolina will vote March 15. Both Florida and Ohio use the winner-take-all method to allocate Republican delegates, making the stakes in those two states particularly high.

If Trump takes Florida and Ohio, he will be nearly impossible to stop. There are a total of 358 delegates at stake in the five states voting March 15, including 99 in Florida and 66 in Ohio.

On the Democratic side, Clinton has opened up a big delegate lead and Sanders might have a tough time making up the difference. All states in the Democratic race award their delegates proportionally, meaning Clinton can keep piling up delegates even in states she loses.

But Sanders made it clear he was not planning to end his White House quest anytime soon.

"We have the momentum. We have a path toward victory. Our campaign is just getting started," he said in a statement after his wins Saturday.

The three states holding Democratic contests Saturday had a total of 109 delegates at stake.