Bernie Sanders refused to concede defeat to Hillary Clinton on Wednesday, vowing to "continue the fight" for the Democratic nomination despite his rival declaring herself the party's flagbearer for the US presidential race.

"Next Tuesday we continue the fight in the last primary in Washington DC," the senator from Vermont told supporters in California. "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.

Sanders appeared to ignore the political writing on the wall, after Clinton surpassed the number of delegates necessary to clinch the party's nomination. Tuesday was the last major date of the 2016 primary calendar, with six states voting.

The former secretary of state extended her delegate lead with wins in New Jersey, New Mexico and South Dakota. Sanders won North Dakota and Montana, US networks said. The grand prize, California, had yet to be called, but Clinton was holding a substantial lead.

Sanders graciously acknowledged Clinton's victories, drawing some boos from the crowd. "Our fight is to transform this country and to understand that we are in this together. To understand that all of what we believe is what the majority of the American people believe," Sanders said.

Sanders by all accounts has conducted an extraordinary grassroots campaign. His supporters are deeply passionate, and Clinton has made it clear she is welcoming any and all of them to her general election campaign as she seeks to defeat Trump.

But Sanders signalled he would want to have an important role not just for keeping the White House in Democratic hands, but in shaping the party's policy platform. "We understand that our mission is more than just defeating Donald Trump, it is transforming our country," Sanders said.

The senator will meet with President Barack Obama at the White House tomorrow to discuss "significant issues at stake in this election that matter most to America's working families," White House press secretary Josh Earnest said in a statement.