Barack Obama has declared himself "the Democratic nominee for president of the United States".
He was speaking to a cheering crowd on the last day of the primary season, as projections showed he had earned enough delegates to clinch the nomination.
Of the states that voted, Montana was won by Mr Obama and South Dakota by his rival Hillary Clinton, US media say.
If confirmed as nominee, Mr Obama would be the first black man to represent a major party in a presidential election.
In her own speech to supporters, Mrs Clinton refused to concede and said she would make a final decision later.
BBC North America editor Justin Webb says a fabulously well-planned and executed campaign helped give him the edge over his rival.
Role for Clinton?
Mr Obama's speech was delivered in St Paul, Minnesota, where Republicans are set to hold their presidential nominating convention
In the address, he paid tribute to Mrs Clinton and hinted that she would play a role in any future Obama administration.
"What gets Hillary Clinton up in the morning is an unyielding desire to improve the lives of ordinary Americans," he said.
"When we finally win the battle for universal healthcare in this country, she will be central to that victory."
Mr Obama also praised Republican rival John McCain's "many accomplishments", although he accused the Arizona senator of choosing to deny his own achievements.
Speaking in New York, Mrs Clinton congratulated Mr Obama and his supporters "for all that they have accomplished".
But she said she was making "no decisions tonight" about her continued presence in the race.
She later spoke to Mr Obama by phone, and he repeated an offer to "sit down when it makes sense to you".
Mr Obama's campaign said she responded positively, though no meeting was expected on Wednesday.
Mr Obama will be tempted to offer Mrs Clinton some inducement to play ball, but may also be tempted to be rid of her and her husband and to strike out on his own, Justin Webb reports.
Earlier, she told congressional backers that she was "open" to the idea of being Mr Obama's vice-presidential running-mate.
Mr Obama was only a few delegates short of the 2,118 needed ahead of the polls closing in South Dakota and Montana.
And although he failed to win in South Dakota, he had managed to pick up enough endorsements during the day from the remaining uncommitted "super-delegates" - party officials with a free choice over who to support - to pass the winning post as soon as polls closed in the state.
His projected victory in Montana added even more delegates to his tally.
In South Dakota, Mrs Clinton won with 55% of the vote to Mr Obama's 45%.
In Montana, with 96% of the results in, Mr Obama had garnered 56% of the vote against Mrs Clinton's 41%.
Before the voting was complete, Republican presumptive nominee John McCain delivered a speech to supporters in Louisiana, in which he declared that "the primary season is over, and the general election campaign has begun".He attacked Mr Obama for being "the wrong change", and defended himself against the Obama campaign's criticism that he will continue President Bush's policies, saying he had "not seen eye to eye" with the president on many issues.
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