WASHINGTON - Mrs Hillary Clinton ended her primary campaign on a high on Tuesday (June 8) night, securing her place in history as the first woman to be the presidential candidate of a major US political party.

Declaring victory in the nomination race, she called the moment a historical "milestone" at a rally in Brooklyn, New York, and said her victory belonged to "generations of women and men who struggled and sacrificed to make this moment possible".

"Thanks to you, we have reached a milestone," Clinton said in a speech. "We all owe so much to who came before."

But her rival, 74-year-old Vermont Senator Bernie Sanders, refused to concede defeat, vowing to stay in the Democratic nomination battle despite his rival declaring herself the party's flagbearer for the US presidential race.

"We are going to fight hard to win the primary in Washington, DC," he told supporters in California, referring to the final nomination contest next Tuesday. "And then we take our fight for social, economic, racial and environmental justice to Philadelphia," where the Democratic convention will be held to formally nominate the party's candidate to challenge Republican Donald Trump for the White House.

President Barack Obama called Mrs Clinton later on Tuesday to congratulate her on becoming the Democratic presidential nominee, the White House said according to Reuters. "Her historic campaign inspired millions and is an extension of her lifelong fight for middle-class families and children,"White House spokesman Josh Earnest said in a statement.

Obama also spoke to Mr Sanders and will meet with him on Thursday at Sanders' request, Earnest said.

Mrs Clinton had the 2,383 delegates needed to clinch the nomination on Monday night, according to media outlets, but chose to wait till Tuesday, after six states including the most populous state of California held their contests, to declare victory.

She won the states of New Mexico, South Dakota and New Jersey, while Mr Sanders won the state of North Dakota. Votes in Montana and California were still being counted.

If Mr Sanders wins the primary in California, it would not be enough for him to catch Mrs Clinton in the overall delegate count but could fuel his continued presence in the race. Mr Sanders has given no indication he plans to concede before the Democratic convention in July.

Mrs Clinton, who needs to enlist Sanders supporters in the looming showdown with Republican Donald Trump, held an olive branch to her rival.

"I want to congratulate Senator Sanders for an extraordinary campaign," the 68-year-old Mrs Clinton said.

"Let there be no mistake, Senator Sanders, his campaign, and the vigorous debate that we've had about how to raise income, reduce inequality, increase upward mobility, have been very good for the democratic party and for America."

"We believe that we are stronger together. And the stakes in this election are high, and the choice is clear," she said.

She then called for unity against Republican presumptive nominee Donald Trump.

"Donald Trump is temperamentally unfit to be president and commander in chief," she told the crowd.

The New York property magnate was not only trying to build a wall between the US and Mexico, but also "trying to wall off Americans from each other", Mrs Clinton added.

Mr Trump had grabbed headlines over the last few days for criticising federal judge Gonzalo P. Curiel, who is presiding over two Trump University lawsuits, saying he was unfair and biased because of his Mexican heritage.

This prompted backlash from the Republican establishment, with House speaker Paul Ryan calling Mr Trump's remarks racist and Republican senator Mark Kirk, from Illinois rescinding his endorsement of real estate billionaire.

Mr Trump, who became the presumptive nominee in early May also spoke on Tuesday, pledging to make his supporters "proud of our party and our movement", but failed to address the controversy directly.

He also reached out to Mr Sanders' supporters by highlighting their shared stance on trade deals such as the 12-nation Trans-Pacific Partnership.

"To those who voted for someone else, I will work hard to earn your support," said Mr Trump in Briarcliff Manor, New York.

"To Bernie Sanders supports...we welcome you with open arms."

Mr Sanders has commanded huge crowds, galvanising younger voters with promises to address economic inequality.

Mrs Clinton is popular among older voters with a more pragmatic campaign focused on building on President Barack Obama's policies, Reuters reported

Mr Steven Acosta, a 47-year-old teacher living in Los Angeles, voted for Mrs Clinton on Tuesday, telling Reuters 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," Mr Acosta was quoted as saying. "The problem is that I think Republicans would really unify... even more against him."