ST. PAUL, Minn. — Before a crowd of cheering thousands, Senator Obama of Illinois laid claim to the Democratic presidential nomination Tuesday night, taking a historic step toward his once-improbable goal of becoming the nation’s first black president. Senator Clinton maneuvered for the vice presidential spot on his fall ticket without conceding her own defeat.

“America, this is our moment,” the 46-year-old senator and one-time community organizer said in his first appearance as the Democratic nominee-in-waiting. “This is our time. Our turn to turn the page on the policies of the past.”

Mr. Obama’s victory set up a five-month campaign with Senator McCain of Arizona, a race between a first-term Senate opponent of the Iraq War and a 71-year-old former Vietnam prisoner of war and staunch supporter of the current American military mission.

And both men seemed eager to begin.

Mr. McCain spoke first, in New Orleans, and he accused his younger rival of voting “to deny funds to the soldiers who have done a brilliant and brave job” in Iraq. It was a reference to 2007 legislation to pay for the Iraq war, a measure Mr. Obama opposed citing the lack of a timetable for withdrawing troops.

Mr. McCain agreed with Mr. Obama that the presidential race would focus on change. “But the choice is between the right change and the wrong change, between going forward and going backward,” he said.

Mr. Obama responded quickly, pausing only long enough to praise Mrs. Clinton for “her strength, her courage and her commitment to the causes that brought us here tonight.”

As for his general election rival, he said, “It’s not change when John McCain decided to stand with George Bush 95 percent of the time, as he did in the Senate last year.

“It’s not change when he offers four more years of Bush economic policies that have failed to create well-paying jobs. … And it’s not change when he promises to continue a policy in Iraq that asks everything of our brave young men and women in uniform and nothing of Iraqi politicians.”

In a symbolic move, Mr. Obama spoke in the same hall — filled to capacity — where Mr. McCain will accept the Republican nomination at his party’s convention in September.

One campaign began as another was ending.

Mrs. Clinton won South Dakota on the final night of the primary season; Mr. Obama took Montana.

The former first lady praised her rival warmly in an appearance before supporters in New York in which she neither acknowledged Mr. Obama’s victory nor offered a concession of any sort.

Instead, she said she was committed to a united party, and said she would spend the next few days determining “how to move forward with the best interests of our country and our party guiding my way.”