Mrs Clinton has ruled out the possibility of her dropping out of the race before all primary and caucus contests were finished.
"We're going to go through the next nine contests and I hope to do well in many of them," she told NBC.
"But I'm confident that when delegates - as well as voters, like the voters of Pennsylvania just did - ask themselves who's the stronger candidate against John McCain that I will be the nominee of the Democratic party."
She told ABC television: "The big win that I had, the broad base of coalition is exactly what we are going to need in the fall [autumn]."
Mr Obama told the audience at a town hall meeting in Indiana not to be worried about the apparently divisive campaigns being fought by the two Democratic candidates.
"The Democratic party is going to recognise that, as soon as we have nominee, there is too much at stake for us to be divided," he said.
"They will see the choice between John McCain and the Democratic nominee and see that there is a clear choice. We know what they are offering - more of the same."
His speech on Wednesday focused more on attacking the policies of Mr McCain than Mrs Clinton.
Exit polls for US media suggest Mrs Clinton won by taking the votes of blue-collar workers, women and white men, the Associated Press reported.
Women - who have tended to favour Mrs Clinton - made up 60% of Democratic voters in the state, according to the exit polls.
Barack Obama is leading the popular vote in the Democratic race
Neither candidate is expected to win sufficient pledged delegates to seal the nomination in the remaining primaries, which is why the candidates are focusing on the 800 or so unelected "super-delegates" to decide the outcome at the Democratic convention in August.
Mrs Clinton has won most of the contests in the big states. She argues that only she will be able to secure wins in critical large states come November's presidential election.
Mr Obama has dismissed the big-state argument, saying there was "no chance" of the Democrats losing New York or California in the presidential election, no matter who the candidate was.
In the next round of primaries, on 6 May, polls suggest that Mr Obama is likely to take North Carolina, while both candidates have a chance to win in Indiana.
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