COLUMBIA, South Carolina (CNN) -- Illinois Sen. Barack Obama claimed a major victory in Saturday's Democratic primary in South Carolina, winning overwhelming support from the state's African-American voters and a significant share among whites, according to exit polls.

Obama's win capped a heated contest in South Carolina, the first Democratic primary in the South and the first with a largely black electorate. Supporters raised thunderous cheers at his campaign headquarters in Columbia after news that his leading rival, New York senator and former first lady Hillary Clinton, had called to congratulate him on his win.

Exit polls estimated Obama took more than 80 percent of the African-American vote, which made up about half of Saturday's turnout. And he had the support of nearly a quarter of white voters, while Clinton and former North Carolina Sen. John Edwards roughly split the remainder.

"This was a very difficult campaign for Barack Obama," said Donna Brazile, a CNN analyst who led former Vice President Al Gore's presidential bid in 2000. "He had an uphill climb. The establishment of the Democratic Party, you know, they're clearly backing Clinton and put tremendous resources in the state to defeat Barack Obama."

With more than half of precincts reporting, Clinton was in second place, while Edwards -- who won his native state in his 2004 White House bid -- ran third.

The win is Obama's second of the primary season, following his January 3 victory in the Iowa caucuses. It follows a rough campaign between Clinton and Obama, who traded barbs with the senator and her husband, former President Bill Clinton, over the past week.

Clinton and Obama battered each other during a Monday debate in Myrtle Beach. Obama criticized Clinton for serving on the board of directors of Wal-Mart while he was a community organizer in Chicago, while Clinton accused Obama of representing a "slum lord" while working as a lawyer there and criticized him for voting "present" numerous times as an Illinois state senator.

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Those exchanges followed a lengthy and sometimes bitter dispute over remarks by members of Clinton's campaign that some voters took as racially insensitive. Clinton accused the Obama campaign of stoking the controversy, while Obama's campaign hit back at a prominent Clinton supporter for raising the issue of Obama's admitted teenage drug use.

Rep. James Clyburn, one of South Carolina's top political figures and the highest-ranking African-American in Congress, said he hoped the candidates can erase the racial tinge to the primary "and go forward talking about the vision that our candidates have."

Noting that the three remaining Democrats split the white vote, he said Saturday's results were a signal that "Everybody ought to just chill, put this stuff behind us and talk about the future." See Clyburn discuss the race »

Obama complained that both his opponent and her husband were attacking him "in ways that are not accurate." Meanwhile, South Carolina native Edwards largely stayed out of the fray and spent the last days of the race campaigning as the "grown-up" alternative. See Edwards make an appeal to voters »

But exit polls showed Obama winning majorities across nearly all demographic groups -- including women, who made up about 60 percent of Saturday's voters and who were a bulwark of Clinton's wins in New Hampshire and Nevada.

Voters listed the ability of a candidate to bring about change as their top quality -- and Obama, who has made that a central theme of his campaign, drew three-quarters of those who picked that as their most important characteristic. Take a look at who voted for whom in the primary

Clinton led the Democratic delegate chase going into South Carolina, largely through the support of "superdelegates" -- elected officials and party leaders. But Saturday's results give Obama new momentum going into "Super Tuesday," the roughly two dozen contests set for February 5.

"This is a great victory for Barack Obama, but this is not the end of the Clinton campaign," Brazile said. "Senator Clinton has broad support out there."

And Clyburn, who has remained neutral in the Democratic race, predicted the campaign would not be settled until the August convention in Denver, Colorado.

"They all have tickets to the convention -- not all first-class, but they all have tickets," he said. E-mail to a friend

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