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He insisted that the votes cast in Democratic primaries were "proof that we have never been more energised and united in our desire to take this country in a new direction" - and not evidence of a divided party.
But the result from Kentucky underlined Mrs Clinton's strength - and Mr Obama's weakness - in a swathe of largely white, rural states cutting across the Appalachian Mountain region.
Exit polls confirmed the Blue Grass state had one of the most conservative electorates among Democratic primaries so far. Mrs Clinton led Mr Obama by a margin of 65 to 30 per cent and almost 250,000 votes in Kentucky.
Surveys showed her attracting almost three-quarters of white women, less-educated whites and older rural voters, as well as two-thirds of church-goers. Two in ten of her supporters openly admitted race had been a factor in their decision.
By contrast, voters in the Oregon primary were among the most liberal and Mr Obama once again harvested the votes of the affluent, young and well-educated in a state which has a tiny proportion of black people.
Perhaps, more significantly, exit polls suggested he also split the votes of the white working class and women - two groups with whom he has struggled to make any connection in recent primaries. With two thirds of the votes counted, Mr Obama was winning by 58 to 42 per cent.
Both primaries were overshadowed to some extent by the news that Senator Edward Kennedy, one of the lions of the Democratic party, had been diagnosed with a malignant brain tumour following the seizure that hospitalised him at the weekend.
Mrs Clinton, in her victory speech, paid tribute to a man she described as "my friend and my inspiration" - even though Mr Kennedy had endorsed her rival for the Democratic nomination earlier this year.
Mr Obama told his rally: "Let us lift his spirits tonight by letting Ted Kennedy know that we are thinking of him, that we are praying for him, that we are standing with him, and that we will be fighting with him every step of the way."
He went on to emphasise that Democrats should prepare for an even fight in the month to come against the Republicans.
"We will face our share of difficult and uncertain days in the journey ahead. The other side knows they have embraced yesterday’s policies and so they will also embrace yesterday’s tactics to try and change the subject," he said. "They will play on our fears and our doubts and our divisions to distract us from what matters to you and your future.
"Well they can take the low road if they want, but it will not lead this country to a better place. And it will not work in this election. It won’t work because you won’t let it. Not this time. Not this year."
Both Democrats are scheduled to visit Florida on Wednesday. Mr Obama has long since planned a three-day sweep through this pivotal state in the last two presidential elections, but Mrs Clinton's late decision to follow him to Florida is widely seen as an attempt to share some of the limelight pouring over her rival.
*Mr Obama's campaign released figures last night showing he has raised more than $31 million last month - and had even more cash on hand. Mrs Clinton, by comparison, is saddled with debts of at least $20 million and while she raised $22 million herself last month, she has been consistently out-spent by her rival not least in both Kentucky and Oregon.
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