ST. PAUL, Minn. — Cheered by a roaring crowd, Sen. Barack 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. Hillary Rodham 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 time to turn the page on the policies of the past."

Obama's victory set up a five-month campaign with Republican Sen. John 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 U.S. military mission.

And both men seemed eager to begin.

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." Americans, he added, should be concerned about the judgment of a presidential candidate who has not traveled to Iraq yet, "says he's ready to talk, in person and without conditions, with tyrants from Havana to Pyongyang."

McCain agreed with 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.

Obama responded quickly, pausing in his own speech long enough to praise 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, Obama spoke in the same hall where McCain will accept the Republican nomination at his party's convention in September. Campaign officials, citing the local fire marshal, put the crowd at 17,000 inside the eXcel Energy Center, plus another 15,000 outside.

McCain addressed a smaller crowd by design, an estimated 600 in his audience and another 600 outside.

One campaign began as another was ending.

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