Republican Donald Trump and Democrat Hillary Clinton scored sweeping victories in nominating contests in their home state of New York, and immediately argued 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.

NO KNOCKOUT PUNCH

Clinton, a former US senator from New York, former secretary of state and former first lady, got nowhere near the knockout punch she needed to finally put Sanders away.

But the broad smile on her face as she gave her victory speech spoke volumes about how important New York was to her bid to become the first female US president.

"Today you proved once again there's no place like home," Clinton said. "This one was personal."

The race for the Democratic nomination, she said, is now in "the home stretch, and victory is in sight."

Clinton, 68, was to campaign in Philadelphia on Wednesday. Sanders flew home to Vermont to take a day off the campaign trail.

Clinton's win made it nearly impossible for Sanders to overtake her commanding lead in the number of delegates needed to win the nomination.

Dilawar Syed, a tech entrepreneur who is also the co-founder and vice chairman of the AAPI Victory Fund, a Super PAC focused on mobilising Asian-American voters, said it looked like Clinton has the nomination.

"Clearly Senator Sanders has a lot of supporters and enthusiasm there. He also has raised a lot of good resources," Syed said. "I think the primary will go on for some time. But just looking at the numbers, we know where this is going." - Reuters