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.
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