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Hillary Clinton is looking to tighten her grip on the Democratic presidential nomination, after an AP count said she had already won enough delegates.
Six states are going to the polls, with California (543 delegates) and New Jersey (142) the big prizes.
Associated Press said Mrs Clinton had already reached the 2,383 delegates needed, taking into account pledges of support from so-called superdelegates.
Rival Bernie Sanders insists it is too early to call the result.
Donald Trump has already secured the Republican nomination.
‘Unprecedented moment’
Voting is also taking place in Democratic primaries in Montana (27 delegates), New Mexico (43) and South Dakota (25), with a caucus in North Dakota (23).
New Jersey was the first state to begin voting
This fire station in Hoboken, New Jersey, was turned into a polling station
AP says its count has Mrs Clinton on 1,812 pledged delegates and 571 superdelegates.
US media organisations say this means she will now become the first female nominee for a major US political party.
Superdelegates are party insiders who can pledge their support for a candidate ahead of the convention but do not formally vote for them until the convention itself.
Analysis – Katty Kay, presenter, BBC World News
It has taken a long 227 years to get even this far.
George Washington was elected president of a newly independent America in 1789. Forty-two men later (41 of them white) Hillary Clinton makes history today by being the first female nominee for the White House.
So why don’t I feel more excited?
The lack of exuberance may come from the fact that this has all been going on for so long.
We’ve really been reworking a version of the “first viable female candidate for the presidency” story since 20 January 2007, the first time Hillary Clinton declared her candidacy for the White House.
We’re exhausted. We’ve run out of superlatives. We’ve overused every anecdote from the former first lady, former senator, former secretary’s well-covered life.
A woman president would be new, Hillary Clinton is not.
Why aren’t we more excited about Clinton?
BBC North America editor Jon Sopel says the AP announcement could actually be a problem for Mrs Clinton, as it may depress turnout in Tuesday’s primaries and creates the impression that she has only won because of the superdelegates and not the ordinary voters.
The Democratic Party has a far larger number of superdelegates than the Republicans, meaning a candidate would have to win 58.8% of primary and caucus votes cast under the party’s proportional system to win by pledged delegates alone. Mrs Clinton has about 55% of the overall vote so far.
She did not claim victory after the AP announcement, telling supporters in Long Beach, California, on Monday: “We are on the brink of a historic and unprecedented moment but we still have work to do.
“We have six elections tomorrow and we’re going to fight hard for every single vote, especially right here in California.”
Mrs Clinton received another boost on Tuesday when the influential Democratic politician and House Minority Leader Nancy Pelosi endorsed her for president.
Outsider’s campaign
Bernie Sanders is hoping for a victory in California to keep his campaign going to the party convention.
Bernie Sanders hopes California will propel him to a party convention showdown
The Vermont senator has commanded huge crowds at his rallies, many of them younger voters, pledging action on income inequality, minimum wages and student tuition fees.
Opinion polls in California have suggested that the race with Mrs Clinton there is close. However, she has a substantial lead in New Jersey.
Reacting to the AP announcement, Sanders team spokesman Michael Briggs said: “It is unfortunate that the media, in a rush to judgement, are ignoring the Democratic National Committee’s clear statement that it is wrong to count the votes of superdelegates before they actually vote at the convention this summer.”
He said Mr Sanders would attempt to win back superdelegates.
But the BBC’s Anthony Zurcher says Mr Sanders has been running an outsider’s anti-establishment campaign that has not generated much enthusiasm among the Democratic power players and long-time party stalwarts who comprise the bulk of the superdelegates.
Also, our correspondent says, success in California hardly helped Mrs Clinton in 2008, when Barack Obama – with the support of superdelegates – defeated her.
AP reports White House officials as saying that Mr Obama is preparing to endorse Mrs Clinton in the next few days, although the announcement would come after Tuesday’s primaries.
Mr Obama telephoned Mr Sanders on Sunday, AP said. The contents of the call have not been revealed.
On 26 May, Donald Trump passed the number of delegates needed to secure the Republican Party’s presidential nomination, AP reported. Republicans are voting in the same states on Tuesday, except for North Dakota.
Mrs Clinton has been saying that Mr Sanders should join her in defeating Mr Trump and hopes for his support soon.
BBC