Donald Trump has won a decisive victory in the key state of Florida but lost to John Kasich in Ohio.
In the Democratic field, 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 Donald Trump.
Donald Trump has also won in Illinois and North Carolina.
Donald 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 with Hillary Clinton locked in tight competition with challenger Bernie Sanders and Donald Trump fighting Ted Cruz.
“We have to bring our party together,” Donald Trump said in Palm Beach, Florida, as the results came in on Tuesday evening.
However, John Kasich secured his first win in the Republican contest in the state of Ohio where he is governor.
In his victory speech, John Kasich said he wanted to create a “climate of opportunity” for future generations and praised the campaign of Marco Rubio.
Earlier Marco Rubio announced he was suspending his campaign on stage in Miami.
He said the US was in the middle of a “political storm”, and voters were angry and frustrated.
In Florida, Hillary Clinton gave an upbeat victory speech in which she chastised Donald Trump and said “Americans were hungry for solutions”.
She listed student debt, affordable childcare and inequality as issues she pledged to address.
Florida and Ohio are particularly important in the race for the Republican nomination because the winning candidate gets all of the delegates on offer – 99 in Florida and 66 in Ohio.
Those delegates go to the national convention in July where the presidential nominee will be chosen.
However, Donald 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 March 15 it emerged that a group of leading conservatives are planning ways of stopping Donald Trump from winning the Republican nomination – including rallying around a third-party candidate.