Hillary Clinton has become the first woman to head a major US party presidential ticket after claiming victory in the Democratic presidential primary race at a campaign rally in Brooklyn.

Clinton’s win over Democrats rival Bernie Sanders was cemented with a victory in New Jersey before polls even closed in California.

The Democratic Party holds its convention in Philadelphia in July to formally choose its nominee for the November 8 election against presumptive Republican nominee Donald Trump.

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“Thanks to you, we’ve reached a milestone, the first time in our nation’s history that a woman will be a major party’s nominee,” she told supporters.

“Tonight’s victory is not about one person. It belongs to generations of women and men who struggled and sacrificed and made this moment possible.”

Mrs Clinton, wife of former president Bill Clinton, was elected as a senator in 2001, making her the first former first lady to win a public office seat.

In 2007 she announced her plans to run for the presidency, but conceded to Barack Obama during the 2008 Democratic primaries.

Mrs Clinton served as secretary of state between 2009 and 2013 in the Obama administration and announced her next bid for the White House in 2015.

New Jersey was one of six states holding contests on Tuesday, along with California – the United States’ most populous state – where she was still at risk of a loss to Mr Sanders as she heads into a campaign against Mr Trump for the November 8 election.

Mr Sanders was projected to win in North Dakota, and there were no immediate projections in Montana, New Mexico or South Dakota in the final series of big presidential nominating battles that began on February 1 in Iowa.

The District of Columbia, the last to vote, holds a Democratic primary next Tuesday.

The delegate count also includes super-delegates, party leaders who can change their minds at any time. Mrs Clinton’s super-delegate support outnumbers Mr Sanders’ by more than 10 to 1.

In a fundraising email to supporters shortly before her appearance in Brooklyn, Mrs Clinton declared her campaign had broken “one of the highest, hardest glass ceilings”.

“Tonight, we can say with pride that, in America, there is no barrier too great and no ceiling too high to break,” she wrote on Twitter. “To every little girl who dreams big: Yes, you can be anything you want – even president. Tonight is for you.”

Mr Trump, meanwhile, has promised to deliver his first major general-election speech next week. He said he would accuse Mrs Clinton and her husband of using their political positions to enrich themselves.

Mrs Clinton’s race against Mr Trump 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 Mrs Clinton’s ratings on honesty and trustworthiness.

– with AAP, ABC