Where many cheered Hillary Clinton's historic victory in the Democratic presidential primary, rival Bernie Sanders vowed to press on with his own "political revolution".

On Tuesday night, the Vermont senator, an insurgent who has rattled the party establishment with a highly effective, populist campaign fighting economic inequality and big vested interests, refused to concede defeat to Clinton.

She is now the presumptive nominee, with more than enough support to be chosen to lead the party's fight against Republican Donald Trump in November.

Sanders's refusal to throw in the towel comes despite the democratic socialist losing four of six state contests on Tuesday. These include delegate-rich New Jersey and, by a much bigger margin than polls had suggested, California.

Sanders had invested everything in California over the past month, appearing at some 40 events.

Clinton has emerged victorious due largely to her landslide victories in big southern states such as Texas and Florida where she has the strong backing of African- and Hispanic-American voters, as well as her strong performances in delegate-rich states such as New York, Pennsylvania and Ohio.

Still, Sanders pledged to continue the contentious Democratic fight right to the party's convention in Philadelphia next month where he wants to convince the "super-delegate" party insiders than he has a better chance of beating Trump.

That may have been theoretically possible two months ago, but Clinton has now claimed a majority of pledged delegates that comes with winning almost four million more popular votes than Sanders.

Stubborn refusal

Tuesday’s election night was a study in political contrasts: the victor gracefully congratulating her opponent “for the extraordinary campaign he has run” and the vanquished stubbornly refusing to accept the inevitable.

Sanders did not mention Clinton until near the end of his speech to supporters in California. They booed her name when he said he had offered his congratulations to her on her victories.

“The struggle continues,” Sanders told the crowd to loud cheers, vowing to “take our fight for social, economic, racial and environmental justice to Philadelphia”.

President Barack Obama gently put his finger on the Democratic scale by congratulating his former secretary of state "for securing the delegates necessary to clinch the Democratic nomination".

Obama’s statement refused to change Sanders’s course. He and the president are due to meet, at the senator’s request, tomorrow.

Even Sanders's only supporter in the US Senate, Oregon Democrat Jeff Merkley, was calling this "the moment when we need to start bringing parts of the party together so they can go into the convention with locked arms".

One prominent Democrat, vice-president Joe Biden, was encouraging the party "to be a little graceful" and give Sanders time to decide on his own.

Undermining himself

For others, the long-time Independent is undermining the unexpected success of his come- from-behind campaign, in which he exploded the prevailing view that the primary would be little more than a coronation for Clinton.

Some argue that Sanders is helping Trump by prolonging a race that he has effectively lost.

“Sanders has won everything but the nomination,” said Democratic strategist Brad Bannon. “He pulled Clinton way to the left. He created a new generation of progressive activists, and he is going to see his imprint all over the party platform. He has won every battle but lost the war.

“If I was him,” Bannon added, “I would quit while I was ahead because it only goes downhill from here. He is in danger of being the guy who helped elect Donald Trump, and he doesn’t want that on his resumé.”

However, the support of grassroots Democrats for an outsider who has won 22 state contests and the backing of 12 million voters on a campaign against a “rigged” political system makes conceding defeat to that system difficult.

Ending the primary fight without losing face as the revolutionary figure of the Democratic presidential primary, or ceding the fired-up, ground-up populist momentum he has built, will be a challenge for the 74-year-old socialist.