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.
“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.
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 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.
Analysis – Anthony Zurcher, BBC News North America Reporter
Donald Trump gave 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.
For the rest of the party faithful – who have watched as their presumptive nominee has been buffeted by allegations that he made racist comments targeting a US judge – they will likely be more inclined to wait and see.
Mr Trump, speaking from a Teleprompter, focused almost exclusively on the kind of economic issues that will play well in the mid-western Rust Belt states where the election will likely be decided. 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.
He also promised to take dead aim at the Clintons, who he said have “turned the politics of personal enrichment into an art form”. Just a week ago Mrs Clinton bludgeoned Mr Trump in a speech where she he was “temperamentally unfit” to be president.
Mr Trump is about to return fire. The general election race is just getting started, and it’s going to be brutal.