Hillary Clinton declared herself the Democratic Party nominee for US president, 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, US senator and 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."

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 November 8 election.

New Jersey was one of six states holding contests on Tuesday, including California, the big prize where Clinton was still at risk of an embarrassing loss to Sanders as she heads into the campaign against Trump.

With about one-third of the votes counted in California, Clinton held a wide 20-percentage-point lead over Sanders, but news networks said the race was still 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 galvanized younger voters.

Clinton edged Sanders out, especially among older voters, with a more pragmatic campaign focused on building on the policies of her fellow Democrat, President Barack Obama.

But Sanders showed no interest in ending his upstart candidacy, telling cheering supporters in California that he would go on campaigning through next Tuesday's primary in the District of Columbia and carry his political crusade - although not necessarily his campaign - to the convention in July.

"We are going to fight hard to win the primary in Washington DC," he said. "And then we take our fight for social, economic, racial and environmental justice to Philadelphia, Pennsylvania."

The White House issued a statement saying 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.

TRUMP 'TEMPERAMENTALLY UNFIT'

In her speech, 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.

Clinton also won in New Mexico and South Dakota. Sanders, 74, won in North Dakota and Montana on the final night of big presidential nominating battles that began on Feb. 1 in Iowa. The District of Columbia will be the last 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 amid 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.

A Reuters/Ipsos poll released on Tuesday showed Clinton leads Trump by 10 percentage points nationally as they launch their general election battle, little changed from a week ago.

PARTY UNITY

Clinton now must try to unify the party and win over Sanders supporters, who booed lustily in California when Sanders congratulated her on her victories on Tuesday.

A Sanders campaign spokesman castigated what he said was the media's "rush to judgment" after the Associated Press and NBC reported on Monday night that Clinton had clinched the number of delegates needed to win the nomination.

Clinton's victories on Tuesday ensured she will have a lead in the pledged delegates won in nominating contests. Clinton clinched the nomination with the added support of superdelegates, party leaders who are free to back any candidate.

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."

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.

"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." - Reuters