He told cheering supporters at a rally in Iowa that they had put him within reach of the nomination. Iowa is the overwhelmingly white state that launched the black, first-term senator from Illinois on his improbable path to victory last January.
Obama lavished praise on Clinton, his rival in a race unlike any other, and accused Republican John McCain of a campaign run by lobbyists.
"You are Democrats who are tired of being divided, Republicans who no longer recognize the party that runs Washington, independents who are hungry for change," he said, speaking to a crowd on the grounds of the Iowa Capitol in Des Moines as well as the millions around the country who will elect the nation's 44th president in November.
Clinton countered with a lopsided win in Kentucky, a victory with scant political value in a race moving inexorably in Obama's direction.
The former first lady vowed to remain in the race, telling supporters, "I'm more than determined than ever to see that every vote is cast and every ballot is counted.
But in a sign of confidence on the front-runner's part, party officials said discussions were under way to send Paul Tewes, a top Obama campaign aide, to the Democratic National Committee to oversee operations for the fall campaign.
And in a fresh sign that their race was coming to an end, Clinton and Obama praised one another and pledged a united party for the general election.
"While we continue to go toe-to-toe for this nomination, we do see eye-to-eye when it comes to uniting our party to elect a Democratic president this fall," said Clinton, whose supporters Obama will need if he is to end eight years of Republican rule in the White House.
Clinton won at least 37 delegates in the two states and Obama won at least 23, according to an analysis of election returns by The Associated Press. All the Kentucky delegates were awarded, but there were still 43 to be allocated in Oregon, and Obama was in line for many of them.
The former first lady's victory in Kentucky was bigger yet -- 65 percent to 30 percent -- and the exit polls underscored once more the work Obama has ahead if he is to win over her voters.
Almost nine in 10 ballots were cast by whites, and the former first lady was winning their support overwhelmingly. She defeated her rival among voters of all age groups and incomes, the college educated and non-college educated, self-described liberals, moderates and conservatives.