Mr Obama was backed by nine in 10 black voters, exit polls suggest
Barack Obama has beaten rival Hillary Clinton to win the Democratic primary election in the state of Mississippi, according to US media projections.
Exit polls suggest he picked up the overwhelming support of the state's many African-American voters.
Mississippi has 33 delegates to the August convention where the party will choose its White House candidate.
Senator John McCain, already the presumptive Republican nominee, is on a nationwide fundraising drive.
Mr McCain, who is set to secure the Republican nomination at the party's national convention in September after winning the backing of a majority of delegates, is under pressure to build up a campaign war-chest ahead of November's election.
Economic problems
According to exit polls for the Associated Press, Mr Obama won the votes of nine out of 10 black voters in Mississippi.
The African-American community made up almost half of the Democratic electorate in the state.
Hillary Clinton has been campaigning hard in Pennsylvania
Mrs Clinton won about two-thirds of the white vote, the exit polls suggest.
The results follow a day of campaigning dominated by a row over remarks on the volatile issue of race made by Geraldine Ferraro, one of Mrs Clinton's fund-raisers.
Ms Ferraro was quoted in a newspaper last week saying: "If Obama was a white man, he would not be in this position."
The New York senator said she regretted the comments, and did not agree with them.
"It's regrettable that any of our supporters - on both sides, because we both have this experience - say things that kind of veer off into the personal," the New York senator told AP on Tuesday. "We ought to keep this on the issues."
Mr Obama had dismissed Mrs Ferraro's comments as "patently absurd", and David Axelrod, one of his senior advisors, had called on her to be removed from the Clinton campaign.
During a final stop in Mississippi before flying to Pennsylvania, the Illinois senator pointed to the economic problems of the Mississippi Delta.
"We just haven't seen as much opportunity come to this area as we'd like," Mr Obama told people gathered at a restaurant in Greenville.
"And one of the challenges, I think, for the next president is making sure that we're serving all communities and not just some communities."
Mr Obama also dismissed Mrs Clinton's offer to run as her vice-president.
Mrs Clinton headed to Pennsylvania on Monday, reflecting the state's importance as the rivals' next major battleground.
The state is due to vote on 22 April, with 158 delegates up for grabs for the Democrats.
Mr Obama has 1,579 delegates in comparison with Mrs Clinton's 1,473, according to the latest tally by the Associated Press.
The successful candidate needs 2,025 delegates to secure the Democratic nomination.
McCain medical check
At a campaign rally in Scranton, Pennsylvania, on Monday, Mrs Clinton refused to be drawn on questions about a close political ally, New York State Governor Eliot Spitzer, who is alleged to have used a prostitution service.
"I don't have any comment on that," she said when asked about allegations he had paid for sex with a prostitute.
"Obviously, I am sending my best wishes and thoughts to the governor and to his family."
Meanwhile, Mr McCain, who has raised less in election funds than either of his Democratic opponents, is touring the country as he seeks to fill his campaign coffers.
He was due to visit New York on Tuesday, followed by trips to Boston, Pennsylvania and Chicago.
Mr McCain had a medical check-up on Monday and declared to reporters that he was free of cancer.
The Arizona senator has faced questions about his health after a bout of skin cancer in 2000.
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