Donald Trump and Hillary Clinton moved a step closer to their parties' nomination with the wins. Photo: AFP/Reuters

Democratic front-runner Hillary Clinton extended her lead with wins in Florida, Ohio, Illinois and North Carolina.

Meanwhile Marco Rubio dropped out of the Republican race after losing in his home state of Florida to Mr Trump.

The billionaire has also won in Illinois and North Carolina.

His victories cause a headache for the Republican party because many senior members are concerned by his policies and tone.

Mr Trump will need just over half of the hundreds of delegates remaining to win a majority in the Republican race and assure him of the nomination.

Five big states on Tuesday chose their preferred candidate for November's presidential election.

The winners for both parties in Missouri are yet to be called. Mrs Clinton is locked in tight competition with challenger Bernie Sanders, while Mr Trump is fighting Ted Cruz.

Mr Trump described the night as "amazing", saying his wins had come despite the fact that "nobody has ever, ever in the history of politics has received the kind of negative advertising that I have".

"My numbers went up," he told a rally in Florida. "I don't understand it. Nobody understands it."

However, he suffered a setback when John Kasich secured his first win in the state of Ohio, where he is governor.

"I will not take the low road to the highest office in the land," Mr Kasich said in his victory speech.

Earlier, Mr Rubio announced on stage in Miami that he was suspending his campaign.

He said the US was in the middle of a "political storm", and voters were angry and frustrated.

Most of the 168 delegates he amassed could get to pick another contender at the Republican convention in July where the nominee is formally chosen.

In Florida, Mrs Clinton gave an upbeat victory speech in which she chastised Mr Trump and said Americans were "hungry for solutions".

"Our commander-in-chief has to be able to defend our country, not embarrass it,'' she said.

Student debt, affordable childcare and inequality were among the issues she pledged to address.

Bernie Sanders congratulated Mrs Clinton but vowed to fight on.

"The reason that we have defied all expectations is that we are doing something very radical in American politics. We are telling the truth," he told supporters in Arizona.

Florida and Ohio are particularly important in the Republican race because the winning candidate gets all of the delegates on offer - 99 in Florida and 66 in Ohio.

But Mr Trump's latest victories come amid increasing condemnation of his campaign within the Republican Party, and after a string of violent incidents at his rallies.

Some senior Republicans have said they would never support him, and on Tuesday it emerged that a group of leading conservatives are planning ways of stopping Mr Trump from winning the nomination - including rallying around a third-party candidate.

"Please join other conservative leaders to strategize how to defeat Donald Trump for the Republican nomination," they wrote in a letter to attendees, according to Politico.