Hillary Clinton has thanked her supporters for helping her reach a historic moment for women – the Democratic nomination for president.
“Thanks to you, we’ve reached a milestone,” she told cheering crowds at a rally in New York.
She hailed “the first time in our nation’s history that a woman will be a major party’s nominee”.
Earlier Mrs Clinton won the Democratic primary in New Jersey, cementing her hold on her party’s nomination.
The AP news agency reported on Monday that Mrs Clinton had enough delegates to qualify as the Democratic nominee.
Six states have been voting in primaries on Tuesday but the race in California will count the most.
Her rival, Bernie Sanders, is hoping for a win in the state, where polls show the race is close.
He aims to sway super delegates to support him instead of Mrs Clinton at the party’s convention in July, but commentators say the Vermont Senator is unlikely to succeed in his bid for the nomination.
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“To every little girl who dreams big: Yes, you can be anything you want—even president. Tonight is for you,” Mrs Clinton tweeted following her win in New Jersey.
Speaking in Brooklyn, New York, she said Republican presumptive nominee Donald Trump was “temperamentally unfit” to be president.
“My mother… taught me to never back down to a bully. Which turned out to be pretty good advice,” she said.
Analysis – Anthony Zurcher, BBC News North America Reporter
In what amounted to a Democratic nomination contest victory speech, Hillary Clinton took some time to acknowledge the historic nature of her achievement. She made reference to the metaphorical glass ceiling that she has now shattered. She referenced the long struggles of the women’s rights movement. And she tipped her hat to her Democratic rival, Bernie Sanders.
Then it was on to the work at hand – wrapping Donald Trump’s recent controversies around his neck and pitching him into the Hudson River.
If Mrs Clinton has run a joyless primary campaign, it has been in part because she’s spent much of it nurturing her built-in advantages within the Democratic Party and playing not to lose. Last week, in a foreign policy speech in San Diego, she went on the attack. And Tuesday night, she continued the broadsides. It’s a role that allows her to show considerably more energy and passion.
Earlier in the evening, Mr Trump, speaking from a Teleprompter, focused almost exclusively on economic issues. Gone were references to Muslim immigration bans or border walls. Instead he made an explicit pitch to Bernie Sanders supporters and other Americans disaffected by the current state of the US political system.
It was the kind of primary night speech that will be well received by Republicans politicians who have spent the last week in a cave or a coma. The rest of the party faithful will likely be more inclined to wait and see.
While Mrs Clinton won in New Jersey and New Mexico, Mr Sanders found victory in the North Dakota caucuses.
Meanwhile Mr Trump won in his party’s vote in New Jersey, South Dakota, New Mexico, California and Montana.
The billionaire turned his attention to the election in November in his remarks at Trump National Golf Club in Briarcliff Manor, New York.
“We’re only getting started and it’s gonna be beautiful,” he said.