Republican Donald Trump and Democrat Hillary Clinton won commanding victories in New York state's US presidential nominating contests on Tuesday, recapturing lost campaign momentum and moving the front-runners closer to their parties' nominations.

The billionaire businessman's huge victory in his home state put Trump in position to win nearly all of the state's 95 delegates, edging closer to the 1,237 delegates needed to win his party's presidential nomination and avoid a contested national convention in July.

Clinton's dominating double-digit primary election win in New York, which she once represented in the US Senate, snapped Democratic rival Bernie Sanders' winning streak and made it nearly impossible for him to overtake her delegate lead.

The victories in one of the biggest state nominating contests so far set up Trump and Clinton for another round of strong performances next Tuesday, when they are expected to do well in five other North-eastern state primaries.

Trump captured about 60 per cent of the vote, easily beating Ohio Governor John Kasich, who got 25 per cent, and US Senator Ted Cruz of Texas, who had 15 per cent, with 95 per cent of the votes counted. For Trump, it was enough to win all 14 state-wide delegates and most of the delegates from each of New York's congressional districts.

“We don't have much of a race anymore based on what I'm seeing on television,” Trump, 69, told cheering supporters at a victory party at his Trump Tower in Manhattan. “We are really, really rocking.”

He said the Republican Party establishment forces that have tried to keep him from a first-ballot victory at the convention are “in trouble,” and repeated his criticism of a “crooked" system that has allowed Cruz to outmanoeuvre him and win delegates in a series of recent state conventions.

Trump entered the New York contest with 756 delegates, while Cruz had 559 and Kasich had 144, according to an Associated Press count. The count includes endorsements from several delegates who are free to support the candidate of their choice.

Trump said his New York win would make it almost mathematically impossible for Cruz, 45, to win the nomination on the first ballot at the party's national convention in July.

If Trump cannot secure enough delegates to win the nomination on the first ballot at the July 18-21 conclave in Cleveland, delegates would be allowed to switch to other candidates.

Some establishment Republicans have been alienated by Trump's more incendiary proposals, such as building a wall along the border with Mexico and temporarily banning Muslims from entering the country.

“We have shown the all-talk, no-action politicians that this is a movement that cannot be stopped,” Trump said in an e-mail to supporters after his win.

'VICTORY IS IN SIGHT'

Clinton's New York victory followed some of the most heated personal exchanges of her political duel with Sanders, a US senator from Vermont and Brooklyn native who had won seven of the last eight state-by-state nominating contests.

“The race for the Democratic nomination is in the home stretch, and victory is in sight,” Clinton, 68, told a cheering, chanting crowd at a Manhattan hotel, noting that she had gained more than 10 million votes and won in every region of the country.

“Today you proved there is no place like home,” Clinton said in a victory speech at a Manhattan hotel that had her looking toward the November 8 election against the eventual Republican nominee.

She reached out to Sanders supporters in what has become an increasingly antagonistic campaign. “There is much more that unites us than divides us,” she said.

But Clinton also could not resist a dig at her rival, repeating language she has used recently to criticise the 74-year-old senator for offering vague policy ideas without a concrete explanation of how he would achieve them.

“In the bright lights of New York we have seen it's not enough to diagnose problems; you have to explain how you actually solve them,” she said.

The New York victory will expand Clinton's lead of 244 pledged delegates over Sanders, and make it nearly impossible for him to overcome the deficit and capture the 2,383 delegates needed for the nomination under Democratic rules that allocate delegates proportionally based on each state's result.

Sanders headed to Pennsylvania to campaign on Tuesday, and then went home to Vermont for a day off the campaign trail.

The voting in New York was marred by irregularities, including more than 125,000 people missing from New York City voter rolls. The city has roughly 4 million voters considered active for the primaries.

New York City Comptroller Scott Stringer ordered an audit of the city elections board after it confirmed the names had been removed from voter rolls. He told the board in a letter it was "consistently disorganised, chaotic and inefficient.”

Addressing supporters at a rally in State College, Pennsylvania, Sanders termed the situation “absurd.”

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