Republican front-runner Donald Trump knocked rival presidential candidate Marco Rubio out of the race with his win in Florida, but was denied a sweep in the five states that held primaries Tuesday by John Kasich, who won his home state of Ohio.

On the Democratic side, former secretary of state Hillary Clinton booked her own easy victories in Florida, North Carolina and Ohio, and a close win in Illinois.

Trump, a New York billionaire and political neophyte who is riding a populist wave, took a big step toward the conservative party's nomination with victories in Rubio's home state of Florida, as well as North Carolina and Illinois.

In the Midwestern state of Missouri, Trump and Clinton both were leading by minute margins - less than 2,000 votes out of more than 600,000 cast in the Democratic primary and 900,000 in the Republican vote. The initial count was completed, but media reports of possible provisional and absentee votes still to be tallied left the outcome unclear.

Florida, the most populous state that voted Tuesday, gave all 99 of its delegates - the party functionaries who will be sent to the Republican convention in July - to Trump.

But Ohio's delegates all went to Kasich, who for the first time finished on top in the state-by-state voting process that began six weeks ago.

In Florida, Trump won 46 per cent to Rubio's 27 per cent. Rubio, who represents Florida in the US Senate, had staked his lagging campaign's survival on winning the state.

Rubio quickly bowed out of the race, saying he had sought to bridge divisions in the country and within the Republican Party, which is bitterly divided over Trump's insurgent campaign and polarizing style.

"While this may not have been the year about a hopeful and optimistic message about our future, I still remain optimistic about our country," he said.

Rubio said the United States had been hit by a "political tsunami" that has left voters "very frustrated about the direction of our country" has taken and tired of being looked down upon by powerful elites in Washington.

On the Democratic side, self-described Democratic socialist Bernie Sanders, who serves as an independent in the US Senate and whose campaign has defied all expectations, was left with little to show Tuesday.

Clinton scored a decisive victory with 65 per cent of the Florida vote, compared to 33 per cent for Sanders, her only opponent for the left-leaning party's presidential nod.

In North Carolina, Clinton won with 55 per cent to Sanders' 41 per cent. She won Ohio with nearly 57 to 43 per cent, and Illinois by almost 51 to 49 per cent.

"We are moving closer to securing the Democratic Party's nomination and winning this election in November," Clinton told cheering supporters.

Trump captured North Carolina with 40 per cent, compared with 37 per cent for second-place candidate US Senator Ted Cruz of Texas. In Illinois, Trump topped Cruz with 39 per cent to 30 per cent.

Kasich, who has been a distant fourth in the national nominating race, was buoyed by his nearly 47 per cent in Ohio, 11 percentage points ahead of Trump.

"We are just all thrilled," Kasich said in an interview with CNN.

He said he aimed to remain positive and not divide the country: "That's why this was such a big victory."

The victory could keep Trump from reaching the Republican convention with an outright majority to win the nomination, depending on results in the coming weeks.

Trump started the day with an early victory when the Republican party on the Mariana Islands reported that he had won the US territory in the Pacific Ocean with 73 per cent.

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