Iowa primary in US presidential election
Republican presidential candidate Donald Trump won convincingly in the New York primary Reuters

Republican Donald Trump and Democrat Hillary Clinton scored sweeping victories in nominating contests in their home state of New York, and immediately cited them in arguing they are all but unstoppable as their respective parties' presidential nominees.

Trump's crushing defeat of Ted Cruz in Tuesday's primary election tilted the energy in the Republican race back to the front-runner, just as Republican National Committee members begin meeting in Florida on Wednesday to discuss their July convention, where the nominee will be chosen.

For the Democratic favourite, Clinton's more narrow victory over Bernie Sanders snapped a string of victories by the 74-year-old democratic socialist and gave her a much-needed lift with more tough fights ahead.

The eventual victors of the Democratic and the Republican nominating campaigns will face each other in November's general election.

Trump's win, celebrated to the tune of Frank Sinatra's "New York, New York" at Trump Tower in Manhattan, marked a rebound from his Wisconsin defeat two weeks ago. It set him up for another big night on April 26, when Pennsylvania, Connecticut, Rhode Island, Delaware, and Maryland will hold primaries.

With a campaign staff reboot and a more focused performance, Trump has sought to improve in recent weeks as a candidate. The tone of his victory speech was in keeping with a more measured style the often-brash billionaire has adopted.

"We don't have much of a race anymore based on what I'm seeing on television," Trump said as television networks projected a large margin of victory for him. "Senator Cruz is just about mathematically eliminated."

Trump, 69, predicted some "amazing weeks" ahead for his campaign.

Still, he has a long way to go to seal the nomination and begin trying to heal the wounds in his bitterly divided party. Some fence-mending may happen when he sends campaign advisers to the RNC meeting starting in Hollywood, Florida, on Wednesday.

Trump's haul of most of New York's 95 delegates moved him closer to the 1,237 needed to win the nomination outright. Anything short of that will lead to a contested convention when Republicans hold their national conclave July 18-21 in Cleveland.

"There's only two issues left for Republicans: Will Trump get 50 percent of the delegates prior to Cleveland, and if not, how close will he be? New York gives him a nice boost, but it will take weeks before we know the answer," said Ari Fleischer, who was White House press secretary under President George W Bush.

Cruz, a 45-year-old US senator from Texas, came in third in New York and gave his primary night speech in Philadelphia, where he was already focused on running in Pennsylvania. He called on Republicans to unite around his candidacy.

Ohio Governor John Kasich, 63, a long-shot candidate, is seeking to use his second-place showing in New York as proof he is emerging as Trump's central challenger in the states that come up next on the calendar.