Democrat Hillary Clinton has beaten rival Bernie Sanders in New Jersey's presidential nominating contest, Fox News projects.

It would add to her lead a day after she captured the number of delegates needed to become her party's US presidential nominee.

Clinton, a former first lady, senator and US Secretary of State, would be the first woman to become the presidential candidate of a major US political party.

New Jersey was one of six states holding contests today, including the big prize of California, where Clinton is still at risk of an embarrassing loss to Sanders as she heads into a campaign against presumptive Republican nominee Donald Trump in the November election.

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Clinton secured enough delegates to the party's convention next month to win the nomination before today's voting, US media outlets reported.

But Clinton campaign manager Robby Mook said the campaign was pushing supporters and volunteers to "stay at this" for the contests in New Jersey, Montana, North Dakota, South Dakota, New Mexico and California.

"We're on the verge of making history, and we're going to celebrate that tonight," Mook told CNN. "There's a lot of people we want to make sure turn out today. We do not want to send a message that anybody's vote doesn't count."

Clinton, who now must try to unify the party and win over Sanders supporters, will highlight the historic nature of her nomination at an event in New York today. Her campaign has compiled a video tying her to women's rights movements in American history. She wants to move beyond the primary battle and turn her attention to Trump.

But Sanders, a democratic socialist US senator from Vermont, has vowed to stay in until July's party convention that formally picks the nominee, defying growing pressure from party leaders to exit the race.

If Sanders wins the primary in California, America's most populous state, it would not be enough for him to catch Clinton in the overall delegate count but could fuel his continued presence in the race.

"We will look forward tonight to marking having reached the threshold of a majority of the pledged delegates," Clinton spokesman Brian Fallon told CNN, referring to delegates won in the state nominating contests. "And at that point, Bernie Sanders will be out of our race."

Sanders has commanded huge crowds, galvanising younger voters with promises to address economic inequality. Clinton has edged him out, particularly 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, 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."

- Reuters