Hillary Clinton took a monumental step toward clinching the Democratic party's White House nomination, while Donald Trump's seemingly unstoppable rush to victory hit a bump in Ohio.

Trump on Tuesday won key Republican primaries in Illinois, North Carolina and Florida -- where he thumped home state Senator Marco Rubio, who immediately announced he was suspending his presidential campaign.

"This was an amazing evening," a buoyant Trump told supporters. "We're going to win, win, win and we're not stopping."

Rubio's loss was a major setback for Republicans trying to stop the bellicose businessman, whose populist anti-immigrant, anti-Muslim stance they fear will split the party.

The 69-year-old Trump was clinging to a narrow lead in Missouri with nearly all of the votes counted, but was denied a clean sweep by Ohio Governor John Kasich, who carried his home state, a key general election battleground.

Trump may now struggle to reach the 1,237 delegates necessary to avoid a challenge at the party's nominating convention in July in Cleveland.

"The bottom line after tonight: it looks like Trump will not have a majority of delegates in July," said Paul Beck, a professor of political science at Ohio State University.

- Big night for Clinton -

There were fewer problems for Clinton, who defeated her rival Bernie Sanders in Florida, North Carolina, Ohio and Illinois. She also had a slight edge in Missouri, according to vote tallies.

Results however were so close -- less than one percent difference -- in Missouri that counting ceased until Wednesday to consider absentee votes and ballots cast abroad, CNN reported. Under state law a recount can be ordered with such close results.

Sanders nevertheless faces an almost impossible task to catch up with Clinton's formidable delegate advantage.

"We are moving closer to securing the Democratic party nomination and winning this election in November," said Clinton, casting one eye on the general election -- and at Trump.

"When we hear a candidate for president call for rounding up 12 million immigrants, banning all Muslims from entering the United States -- when he embraces torture, that doesn't make him strong. It makes him wrong."

Sanders however was not giving up. He congratulated Clinton on her Tuesday victories in a statement, but added that with more than half the delegates "yet to be chosen and a calendar that favors us... we remain confident that our campaign is on a path to win the nomination."

Republicans will now have to decide whether to rally behind one candidate or siphon votes away from Trump as a team.

The scope of Trump's victory against Rubio in Florida will shock the Republican establishment as much as it will raise hopes the party can challenge in the one-time swing state come November 8.

President Barack Obama carried the state in both the 2008 and 2012 elections.

Rubio bowed out, saying: "While it is not God's plan that I be president in 2016 or maybe ever, and while today my campaign is suspended, the fact that I've even come this far is evidence of how special America truly is."

Kasich meanwhile openly called for a contested convention and vowed to campaign on.

"I want to remind you, again tonight, that I will not take the low road to the highest office in the land," he said.

Ted Cruz, an ultra-conservative senator from Texas, also remains in the Republican race.

Projections by US media showed him just behind Trump in Missouri, and in second place in Illinois and North Carolina.

Cruz made a call for Republicans to unify behind him against Trump.

"Donald may be the one person on the face of the earth that Hillary Clinton can beat in the general election," he said, telling Republicans they now face "a clear choice."

- 'Vulgar and divisive' -

Trump's incendiary attacks on immigrants, threats of mass deportations and a proposal for a wall on the border with Mexico have ignited the campaign trail and drawn condemnation in some quarters -- the latest being from President Barack Obama.

Without pointing the finger directly at Trump, Obama professed to being "dismayed" at some of the comments during campaigning.

"We have heard vulgar and divisive rhetoric aimed at women and minorities -- at Americans who don't look like 'us,' or pray like 'us,' or vote like we do," said the president, who along with his wife Michelle cast absentee ballots in their home state of Illinois.

But Trump's populist message has resonated -- even with some Democrats like 69-year-old Katharine Berry.

"We don't need all these illegals," she told AFP outside a polling station at the Zion Lutheran Church in Canton. "They're taking our jobs, they've got all these rights, Americans don't have rights.

"I voted Democrat today. But if Trump wins, then I'm going to vote for him in the general election."