Powered by solid returns in California, Hillary Clinton has declared victory in her yearlong battle for the heart of the Democratic Party, seizing her place in history and setting out on the difficult task of fusing a fractured party to confront Donald Trump.

Clinton cruised to easy victories in four of the six state contests on Tuesday and, by Wednesday morning with some 70 per cent of the votes in, she was projected by CNN to have won California.

With each victory, she further cemented Senator Bernie Sanders' defeat and dashed his already slim chances of using the last night of state contests to refuel his flagging bid.

The victories allowed Clinton to celebrate her long-sought "milestone" — the first woman poised to lead a major political party's presidential ticket. Standing before a flag-waving crowd in Brooklyn, the former secretary of state soaked up the cheers and beamed.

"We are all standing under a glass ceiling right now," she told her boisterous supporters.

"Barriers can come down. Justice and equality can win," she said. "This campaign is about making sure there are no ceilings, no limits on any of us. This is our moment to come together."

"Tonight's victory is not about one person," Clinton added. "It belongs to generations of women and men who struggled and sacrificed and made this moment possible."

She had already secured the delegates and superdelegates needed for the nomination after a Puerto Rico primary won on the weekend, according to tallies by the Associated Press and NBC News.

It's clear tonight that this fall's US election will - for the first time in American history - feature a woman running for the top job, for one of the main parties. 2:38

Clinton also won Tuesday in New Jersey, New Mexico and South Dakota, with Sanders victorious in the North Dakota caucus and Montana. With the win in California, Clinton has won 16 of the 20 most populous states through the primary season.

President Barack Obama, her rival in the 2008 Democratic race, called Clinton to congratulate her for securing "the delegates necessary to clinch" the nomination for president.

But the president did not formally endorse Clinton. Obama also called Sanders to praise him for shining a spotlight on economic inequality and energizing millions of voters.

The statement said that Sanders requested a meeting with Obama, which will occur Thursday at the White House.

Clinton and Sanders are also expected to connect in the coming days, Clinton's spokesman said late Tuesday. The candidates' campaign managers spoke earlier in the day, signalling that conversations were underway about the road ahead.

Democratic presidential candidate Senator Bernie Sanders assured supporters at Santa Monica, Calif., he would press on his campaign, despite math from the news organizations indicating that Hillary Clinton has the needed delegates to secure the nomination. (Scott Olson/Getty Images)

But Sanders was not ready for his concession when he spoke just before 11 p.m. local time in California, vowing to contest next week's contest in D.C. and continue the fight to the party convention in Philadelphia, pointing to wins in 22 states.

"I am pretty good at arithmetic. I know that the fight in front of us is a very, very steep fight, but we will continue to fight for every vote and every delegate," he said.

Based on primaries and caucuses to date, not including California, Clinton has now won 1,898 delegates to Sanders' 1,589.

Her lead is bigger when including superdelegates, 2,469 to Sanders' 1,637. The number needed to secure the nomination is 2,383.

Superdelegates are able to change their vote at the convention, although the last time they were a significant factor in putting a candidate over the top to determine the Democratic winner was in 1984.

Sen. Claire McCaskill, D-Mo., said that for Sanders "I think the math is unforgiving," as a report in the New York Times indicated that the Vermont senator could be laying off a significant number of staff on Wednesday.

Clinton had praised Sanders for the "extraordinary" campaign and his ability to excite "millions of voters, especially young people." The former state senator and secretary of state said Sanders raised the bar on debate during the primary season for the Democrats.

She made a pitch for his supporters: "It never feels good to put our heart into a cause or a candidate you believe in and come up short ... But as we look ahead to the battle that awaits, let's remember all that unites us."

She deemed Trump "temperamentally unfit" to be president, citing his attacks on a federal judge, reporters and women.

To every little girl who dreams big: Yes, you can be anything you want—even president. Tonight is for you. -H <a href="https://t.co/jq7fKlfwGV">pic.twitter.com/jq7fKlfwGV</a> —@HillaryClinton

Trump, too, makes appeal to Sanders' voters

In San Diego, 82-year-old Harry Backer strolled past cyclists, skateboarders and kayakers on the way to vote for Clinton. The retired teacher, who also worked in construction, said America needs a level-headed, grounded woman with world experience.

"I'm left of Bernie Sanders, but I know that she's the candidate that can possibly get something done," Backer said.

He also wanted to be part of history in making Clinton the first woman to top the ticket of a major U.S. political party.

In Albuquerque, N.M., Lucy Demir voted for Sanders.

"I like him because he's really honest," said Demir, 37. "I think he's really direct, and I appreciate how he really is trying to stay on his side of the street. I actually think some of his ideals are kind of like utopic and he's probably not going to achieve them, but I like his character."

In Closter, N.J., an upscale suburb, Izabela Biel voted for Trump, saying his success as a businessman symbolizes the American dream for her. Biel came to the U.S. from Poland about 25 years ago, and she said that even though he isn't the perfect candidate, she prefers him to the Democratic candidates, who "want to make everybody equal."

Republican presidential candidate Donald Trump used a victory speech Tuesday to attack likely Democratic candidate Hillary Clinton, saying she used the State Department as 'own private hedge fund." (MartAssociated Press)

"I grew up in communism," said Biel, 46. "I've lived it, and I absolutely know that it's proven that it doesn't work. You can't make everybody equal; that just doesn't exist in the real world."

The Democratic race seemed to be coming to a conclusion amid new turmoil among the Republicans. GOP leaders recoiled at Trump's comments about a Hispanic judge, with one senator even pulling his endorsement.

Trump capped his difficult day with victories in California, New Jersey, New Mexico, South Dakota and Montana. He was muted his victory rally, saying he understands "the responsibility" of leading the Republican Party. He also made a direct appeal to dejected Sanders supporters and other Democrats.

"This election isn't about Republican or Democrat, it's about who runs this country: the special interests or the people," he said. Trump vowed to deliver a major speech next week on Clinton and her husband, former President Bill Clinton.

In contrast to some previous speeches, Trump was often restrained and used a teleprompter.

Trump won at least 297 delegates in Tuesday's primaries. Six delegates in California are still left to be allocated because of incomplete results in individual congressional districts.