LOS ANGELES: Hillary Clinton declared herself the Democratic Party nominee for United States president on Tuesday, embracing her role in history as the first woman to lead a major party in a race for the White House.

The former first lady, senator and US secretary of state celebrated her victory in the nominating race over rival Bernie Sanders at a raucous event with supporters in Brooklyn, New York, where Clinton placed her achievement in the context of the long history of the women's rights movement.

“Thanks to you, we have reached a milestone,” Clinton said in a speech. “We all owe so much to who came before.”

New Jersey win, North Dakota loss

Clinton, 68, spoke shortly after beating Sanders in New Jersey's nominating contest, expanding her lead in the delegates needed to clinch the nomination and setting up a five-month general election campaign against presumptive Republican nominee Donald Trump in the Nov 8 election.

Clinton also won the presidential primary in New Mexico and South Dakota, walking away with three wins in Tuesday's half dozen contests against rival Bernie Sanders, who won in North Dakota and Montana.

Among the six contests taking place on Tuesday is California, the big prize where Clinton was still at risk of an embarrassing loss to Sanders.

Polls in California closed at 11 p.m. ET, but news networks said the race was too close to call.

In her speech, Clinton appealed to Sanders supporters to join her and said the Democratic Party had been bolstered by his campaign for eradicating income inequality, which has commanded huge crowds and galvanised younger voters.

By contrast, Clinton harshly attacked Trump for using divisive rhetoric that belittled women, Muslims and immigrants, and took specific aim at his recent condemnation of an Indiana-born judge of Mexican heritage.

“The stakes in this election are high and the choice is clear. Donald Trump is temperamentally unfit to be president and commander-in-chief,” she said.

“When Donald Trump says a distinguished judge born in Indiana can't do his job because of his Mexican heritage, or he mocks a reporter with disabilities, or calls women pigs, it goes against everything we stand for,” she said.

'Glass ceiling'

There were no immediate projections in Montana or South Dakota in the final series of big presidential nominating battles that began on Feb 1 in Iowa. The District of Columbia, the last to vote, holds a Democratic primary next Tuesday.

In a fundraising email to supporters, Clinton declared her campaign had broken “one of the highest, hardest glass ceilings.”

On Twitter, she said: “To every little girl who dreams big: Yes, you can be anything you want - even president. Tonight is for you.”

Clinton's race against Trump, 69, will unfold as she faces an ongoing investigation of her use of a personal email server while secretary of state. Opinion polls show the controversy has hurt Clinton's ratings on honesty and trustworthiness.

Clinton now must try to unify the party and win over Sanders supporters after a bruising primary battle. But Sanders, a democratic socialist US senator from Vermont, has vowed to stay in the race until July's party convention that formally picks the nominee, defying growing pressure from party leaders to exit the race.

Although Sanders will be unable to catch Clinton even if he wins the primary in California, America's most populous state, a triumph there could fuel his continued presence in the race and underscore Clinton's weaknesses as she heads into the fight with Trump.

The White House issued a statement saying President Obama had called both Clinton and Sanders. It said he congratulated her on securing the delegates necessary to clinch the nomination and would meet Sanders on Thursday at Sanders' request.

Clinton edged Sanders out, especially among older voters, with a more pragmatic campaign focused on building on President Barack Obama's policies.

Steven Acosta, a 47-year-old teacher living in Los Angeles, voted for Clinton on Tuesday, saying that was partly because he believed she stood a better chance of winning in November.

“I like what Bernie Sanders says and I agree with almost everything that he says,” Acosta said. “The problem is that I think Republicans would really unify ... even more against him.”

'Rush to judgment'

Sanders was determined to stay in the race, even after the Associated Press and NBC reported on Monday night that Clinton had clinched the number of delegates needed to win the nomination.

A Sanders campaign spokesman castigated what he said was the media's “rush to judgment".

Under Democratic National Committee rules, most delegates to the July 25-28 convention in Philadelphia are awarded by popular votes in state-by-state elections, and Clinton has a clear lead in those pledged delegates.

But the delegate count also includes superdelegates, party leaders who can change their minds at any time. Clinton's superdelegate support outnumbers Sanders' by more than 10 to 1.

The Sanders' campaign has said it can still persuade superdelegates to switch to him, although in practice superdelegates who have announced their intentions are unlikely to change their minds.

Sanders would have to get more than 60 per cent of the superdelegates backing Clinton to switch their votes. So far, his campaign manager, Jeff Weaver, acknowledged they had yet to convert a single delegate.

Trump, who became his party's presumptive nominee last month, outlasting 16 Republican challengers, is struggling to get the party's leaders solidly behind him after a bitter primary campaign during which he made a series of controversial statements directed at Muslims, Latinos, women and the disabled.

On Tuesday night he addressed a crowd of supporters in New York, welcoming Sanders supporters “with open arms” should they decide to support him and declaring a new phase of the campaign had begun.

“Tonight we close one chapter in history and we begin another,” Trump said.

“I am going to give a major speech on probably Monday of next week, and we are going to be discussing all of the things that have taken place with the Clintons,” he said.

“I think you are going to find it very informative and very, very interesting. I wonder if the press will want to attend.”