Donald Trump has scored victories in three states, including the big prize of Florida, but lost Ohio to state governor John Kasich, as the billionaire's rivals desperately tried to stop his march to the Republican presidential nomination.

Marco Rubio, the Florida senator who staked his once-promising campaign on winning in his home state, dropped out of the presidential race shortly after the polls closed, leaving Mr Kasich as the last true establishment candidate running against Mr Trump and arch-conservative Ted Cruz.

Hillary Clinton won at least four states, dealing a severe blow to the bid by Bernie Sanders to slow her march towards the Democratic nomination.

Mr Trump, the controversial reality TV star, has upended the political establishment by winning most of the state-by-state competitions for delegates who will choose the Republican nominee. He has seized on Americans' anger with Washington politicians, attracting voters with his simply worded promise to make America great again.

Tuesday's votes in five states had been viewed as a pivotal moment in the Republican presidential campaign. For the first time, two states - Ohio and Florida - had winner-take-all contests.

A Trump sweep could have given him an insurmountable lead in the delegate count, but the contests brought little clarity. He won the biggest prize - all 99 Florida delegates - as well as winning North Carolina and Illinois, and was locked in a tight race with Mr Cruz in Missouri. He told a victory rally in Florida: "This was an amazing night."

But Mr Kasich's win, capturing all of Ohio's 66 delegates, was crucial to keeping alive the hopes of those trying to stop Mr Trump.

While the New Yorker had amassed the most delegates going into Tuesday, he has won fewer than 50%. If that pace continued, he would fall short of the majority he would need to assure him the nomination at the party's convention in July. The result could be a contested convention, creating an unpredictable outcome.

This was the first victory for Mr Kasich, whose upbeat message and long record of government service has had little resonance as his rivals seized on voter anxiety and disdain for Washington. While he could benefit from Mr Rubio dropping out, he remains a long shot for the nomination. He is unlikely to overtake Mr Trump, though he could help keep him below the 50% threshold.

Mr Cruz said at a Houston rally that the battle for the Republican presidential nomination battle was a "two-person race".

Mr Trump now has 619 delegates, while Mr Cruz has 394, Mr Kasich 136 and Mr Rubio left the race with 167. It takes 1,237 delegates to win the Republican nomination for president.

In the Democratic race, Ms Clinton scored victories in Florida, Ohio, Illinois and North Carolina. Mr Sanders, a Vermont senator and self-described democratic socialist, is unlikely to overtake her in the delegate count, but his victory last week in Michigan underscored the unease many party voters have about her candidacy.

Her wins on Tuesday, put Ms Clinton in a commanding position to become the first woman in US history to win a major party nomination.

At a victory rally in West Palm Beach, Florida, Ms Clinton pivoted quickly to the November election by assailing Mr Trump's hardline immigration positions and support for torture. "Our commander-in-chief has to be able to defend our country, not embarrass it," she said.

Mr Trump has alienated many Republicans and Democrats with his disparaging remarks about Mexicans, Muslims and women, among others. He entered Tuesday's primaries embroiled in one of the biggest controversies of his campaign. He has encouraged supporters to confront protesters at his events and is facing accusations of encouraging violence after skirmishes at a rally last week in Chicago that he ended up cancelling.

"I don't think I should be toning it down because I've had the biggest rallies of anybody probably ever," Mr Trump said on ABC's Good Morning America. ''We have had very, very little difficultly."

Mr Rubio and Mr Kasich have suggested they might not support Mr Trump if he is the nominee.

Mr Rubio implicitly rebuked Mr Trump throughout a speech in Miami announcing he was dropping out of the race, imploring Americans to "not give in to the fear, do not give in to the frustration".

Now thrust into the centre of a campaign that has been bitingly personal, Mr Kasich vowed to cheering supporters in Berea, Ohio, that he would "not take the low road to the highest office in the land".

With 98.8% of precincts reporting in Missouri, both the Republican and Democratic races in the state are too close to call.

The margins in the contests between Mr Trump and Mr Cruz and Ms Clinton and Mr Sanders are less than 0.5%, which means the losing candidate can request a recount.