Hillary Clinton celebrates 'milestone' victory as Sanders refuses to end bid

But on a night when it became clear that Clinton would secure a majority of pledged delegates, Sanders refused to bow out, telling supporters that their fight would continue to the Democratic National Convention in July.

The senator’s defiant remarks came after Clinton effectively declared victory in her overall battle against Sanders at a rally in New York.

Clinton told supporters that she had "reached a milestone” as the first woman to be a major party’s nominee for president, and immediately framed November’s general election as a contest between two opposing visions of the future.

"He’s not just trying to build a wall between America and Mexico, he’s trying to wall off Americans from each other,” Clinton said, taking aim at the policies and slogans that have become the hallmark of her Republican rival, Donald Trump. "When he says let’s make America great again, that is code for let’s take America backwards.”

In her speech, Clinton praised Sanders for exciting "millions of voters, especially young people” in what she said was an "extraordinary campaign”.

"I know it never feels good to put your heart into a cause or a candidate you believe in and come up short,” she said, referring to her defeat to Barack Obama in 2008. "I know that feeling well.”

Sanders had been pinning his hopes on an upset in California, the most delegate-rich contest on the primary calendar, and one where polls had recently shown him neck and neck against Clinton. In the early hours of Wednesday, with 63.2% of precincts reporting and the race not yet called, Clinton had 57.3% compared with Sanders’ 41.7%.

She had also won New Jersey, New Mexico and South Dakota, while Sanders had triumphed in North Dakota and Montana.

On the Republican side, Trump remained mired in a remarkable clash with the most senior members of his party, including the leaders of the House and the Senate, some of whom were effectively accusing the nominee they have just endorsed of outright racism.

Promising to continue all the way to the July convention, he added: "And then we take our fight for social, economic, racial and environmental justice to Philadelphia.”

However, the short speech from Sanders, amid reports that he plans to lay off up to half his staff on Wednesday, added to the expectation that his campaign may soon wind down.

Obama, who is said to be planning to endorse Clinton in the coming days, is expected to play a mediating role between the Democratic adversaries after their bruising campaigns. The president called both candidates after polls had closed, the White House said, and plans to meet with Sanders on Thursday.

Clinton claimed the mantle of the Democratic nominee exactly eight years to the day after she conceded defeat in her campaign against then senator Obama, memorably telling supporters that she had fallen short in her quest to shatter "that highest, hardest glass ceiling”.

On Tuesday, she returned to that metaphor, telling ecstatic supporters that the ceiling above them, in the Brooklyn Navy Yard, was made of glass. "But don’t worry,” she said. "We’re not smashing this one. Thanks to you, we’ve reached a milestone. The first time in our nation’s history that a woman will be a major party’s nominee.”