ST. PAUL, Minn. | Barack Obama claimed the Democratic presidential nomination in a long-time-coming victory speech Tuesday that taunted Republicans on their own turf and reached out to heal Democratic wounds with lofty praise for his rival.

"Let us begin the work together," Obama exhorted thousands of cheering supporters in a packed sports arena. "Let us unite in common effort to chart a new course for America."

Speaking in the same arena that will host the Republican nominating convention in early September, Obama said the long, hard primary campaign, now finally ended, should help steel a deeply divided party to do more effective battle against Republicans and their candidate, John McCain.

"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," Obama said.

"Our party and our country are better off because of her, and I am a better candidate for having had the honor to compete" with her, he said.

Speculation spread over whether he would invite her to share the ticket as his running mate, and Clinton only encouraged it. But Obama aides tied to tamp down such talk.

"We don't have a long list or a short list," said David Axelrod, Obama's chief strategist. "Obviously she's an incredibly formidable person. We knew that going in. It's way too early to talk about that."

Obama won a mathematical lock on the nomination as previously undeclared superdelegates -- elected and party officials -- flocked to his side on the day of the last presidential primaries. Still, Clinton did not concede her own defeat.