Senator Obama’s declared victory in the Democratic presidential primary last night sets the stage for a fall general election campaign that will pit the nation’s first black major party nominee against a decorated war hero, Senator McCain of Arizona.

The freshman Illinois senator clinched the nomination on the final day of primaries by securing the support of enough Democratic leaders to mathematically defeat Senator Clinton after an epic, bruising battle for the top slot on the party’s November ticket.

Mr. Obama claimed the triumph before a crowd of thousands in St. Paul, Minn., where he called for party unity and lavished praise on Mrs. Clinton, his vanquished opponent whose support he will need to win the presidency this fall.

“Tonight we mark the end of one historic journey with the beginning of another,” Mr. Obama told supporters packed into the arena where Republicans will hold their nominating convention in September. “Because of you, tonight, I can stand before you and say that I will be the Democratic nominee for president of the United States.”

Of the former first lady, he said: “Senator Hillary Clinton has made history in this campaign not just because she’s a woman who has done what no woman has done before, but because she’s a leader who inspires millions of Americans with her strength, her courage, and her commitment to the causes that brought us here tonight.”

Mr. Obama characterized the upcoming election as a seminal moment and called on Americans to summon the same spirit to confront the current challenges that spurred the nation in world wars and the civil rights movement. “So it has been for every generation that faced down the greatest challenges and the most improbable odds to leave their children a world that’s better, and kinder, and more just,” he said, raising his voice to a crescendo. “And so it must be for us. America, this is our moment. This is our time, our time to turn the page on the policies of the past.”

Laying out his case against Mr. McCain, Mr. Obama saluted the Arizona senator’s military service while disputing his attempts to campaign as a political maverick. “There are many words to describe John McCain’s attempt to pass off his embrace of George Bush’s policies as bipartisan and new,” Mr. Obama said.

His speech cast the primary fight as over, even though Mrs. Clinton has not exited the race.

Appearing before hundreds of boisterous supporters in New York, she praised and congratulated Mr. Obama on his campaign but pointedly refused to acknowledge his nomination.

“This has been a long campaign, and I will be making no decisions tonight,” she said to cheers at Baruch College on Manhattan’s East Side, adding that she would consult Democratic leaders and choose her next move “with the best interests of our party and our country” in mind.

She urged supporters to advise her with notes on her Web site, and the crowd gathered last night responded with a clear message: Fight on. Cheering heartily through the speech, the throng interrupted Mrs. Clinton at one point with chants of “Denver! Denver!” — a reference to the site of the Democratic National Convention this summer.

While offering no specific hint of her plans, Mrs. Clinton confronted directly the question on the minds of Democrats across the country. “I understand that a lot of people are asking, ‘What does Hillary want? What does she want?’ Well, I want what I have fought for this whole campaign,” she said, before reciting a wish list of top policy items, beginning with her signature issue: universal health care. She made no mention of the vice presidency or any other post.

The two candidates split the final two primaries yesterday, with Mr. Obama winning Montana and Mrs. Clinton capturing South Dakota.

Meanwhile, Mr. McCain delivered a televised address from a suburb of New Orleans before either Democrat spoke, in a speech that his campaign said was aimed at kicking off the general election race in earnest and framing a stark contrast with Mr. Obama.

After praising Mrs. Clinton’s “tenacity and courage,” Mr. McCain set his sights on Mr. Obama, criticizing the Democrat’s experience and judgment on a range of foreign and domestic issues. While presenting himself as a forward-looking candidate with a nonideological vision, Mr. McCain said Mr. Obama had adopted big-government policies that have failed in the past. ‘That’s not change we can believe in,” he repeated in a riff on the Obama campaign slogan.

He also questioned Mr. Obama’s claim to a record of forging unity and working across the party aisle.

“Both Senator Obama and I promise we will end Washington’s stagnant, unproductive partisanship. But one of us has a record of working to do that and one of us doesn’t,” Mr. McCain said. “Americans have seen me put aside partisan and personal interests to move this country forward. They haven’t seen Senator Obama do the same.”

“He is an impressive man, who makes a great first impression,” he added. “But he hasn’t been willing to make the tough calls; to challenge his party; to risk criticism from his supporters to bring real change to Washington. I have.”

Belittling Mr. Obama’s effort to link him at every turn with President Bush, Mr. McCain explicitly distanced himself from the current administration. “I have worked the with the president to keep our nation safe, but he and I have not seen eye to eye on many issues,” he said.

The speeches capped an eventful day in which Democratic superdelegates announced their support for Mr. Obama literally by the hour, forcing Mrs. Clinton to contemplate a concession. As the endorsements mounted, it became clear that Mr. Obama would reach the 2,118 delegates needed to secure the nomination by the time he took the stage in St. Paul.

In an afternoon conference call, she told members of the New York congressional delegation — a group of her most loyal supporters — that she would not concede last night and thought she deserved the right to examine her options, according to a participant on the call.

After furiously denying a report that Mrs. Clinton would drop out of the race, her campaign continued to compete throughout the day, even announcing the support of a Wyoming superdelegate as late as 8 p.m.

She is scheduled to address the American Israel Public Affairs Committee this morning in Washington.

The lingering divisions within the Democratic Party were on full display last night as Mrs. Clinton’s supporters rallied before her speech in Manhattan and pushed her to keep fighting through the nomination convention this summer. Crowds loudly chanted “Denver! Denver!” and “No Hillary, No Vote!.”

Some supporters flatly insisted they would not vote for Senator Obama under any circumstances, including an endorsement by Mrs. Clinton.

“I have always voted Democratic but this year I will not pull the lever for the top of the ticket,” a Clinton volunteer, Linda Leest, 64, said.

Republican leaders signaled they would compete aggressively for Clinton supporters, issuing a strategy memo outlining Mr. Obama’s weakness with key constituencies, including older voters, the working class, and Hispanics.