By John Whitesides and Ellen Wulfhorst

COLUMBIA, South Carolina (Reuters) - Democrats Barack Obama, Hillary Clinton and John Edwards honored the legacy of slain U.S. civil rights leader Martin Luther King on Monday and said his work paved the way for this year's precedent-shattering White House candidacies.

Obama, who would be the first black U.S. president, and Clinton. who would be the first woman U.S. president, joined Edwards at a rally outside the South Carolina state capitol in a hunt for black support on the holiday marking King's birthday.

The Republican presidential contenders flooded Florida ahead of a crucial showdown on January 29 in a nomination race where three different candidates have scored wins and a fourth, Rudy Giuliani, is looking for his big breakthrough.

For Democrats, South Carolina is the next battleground in a seesawing race to find a candidate for the November election. Obama holds a slim lead in polls in the state, where more than half of the likely primary voters on Saturday will be black.

"Let us just take a moment to marvel at the progress we have made together," Clinton, a New York senator, told more than 5,000 people on the lawn of the capitol.

She said the rally was a testament to King's efforts to knock down social barriers and bring justice to those who lived on the margins. "But the work is far from finished," Clinton said. "The dream is not fulfilled."

Obama, an Illinois senator, marched to the rally with about 1,000 people through downtown Columbia, walking alongside a group of Clinton supporters chanting her name. Once there, the crowd gathered beneath a Confederate flag that once flew on the statehouse.

"It's not always easy to see past our differences," Obama said, with Clinton and Edwards seated on stage behind him. "Every day our politics fuels and explores these kinds of divisions."

Edwards, who was born in South Carolina and won the state primary during his failed White House bid in 2004, said he was proud to be on the stage with a black and a woman presidential candidate.

MARCH TO JUSTICE

"All three of us are on the journey with you on the march to justice and equality," said Edwards, who has promised to push on in the race despite distant third-place finishes in New Hampshire and Nevada.

The three Democratic contenders will meet in a debate in Myrtle Beach, South Carolina, later on Monday night.

Clinton will leave the state after the debate for two days of campaigning in California, Arizona, New Mexico and New Jersey, states that vote during the February 5 "Super Tuesday" round of 22 contests.

Across the street from the rally, about a dozen protesters held signs picturing the Confederate flag and reading "Yankee Go Home" and "The Flag Stays."

Neither party has established a clear front-runner in the race to pick the two candidates to contest the November 4 election to succeed President George W. Bush, as the first major state-by-state battles produced multiple winners.

Mitt Romney, the former Massachusetts governor who won Republican contests in Michigan and Nevada, also cited King's work during a campaign stop in Jacksonville, Florida.

"Sometime you think problems are huge and they're beyond the scope of anyone's ability to deal with them, but an individual of passion and courage and faith and character can help change an entire nation, as he did," Romney said.

Romney is in a tight race in Florida with Arizona Sen. John McCain, who won last Saturday's Republican primary in South Carolina and earlier in New Hampshire, former Arkansas Gov. Mike Huckabee, who won Iowa, and Giuliani.

Giuliani sat out the early voting states in order to concentrate on Florida in hopes it will propel him on to the February 5 "Super Tuesday" voting with fresh momentum.

McCain wooed Cuban-American voters in Miami and told that influential bloc of Republican voters he would not lift the trade embargo on Cuba until it holds free elections.

Huckabee attended on Monday King's home church in Atlanta, Ebenezer Baptist Church, before heading to Florida. Obama spoke at the Atlanta church on Sunday.

The Democrats also are holding a primary in Florida, but because of a dispute between the state and national parties the candidates have pledged not to campaign there.

The Clinton campaign said it would re-evaluate that pledge, however, after Obama bought a national ad on cable television that will be aired in Florida.

(Additional reporting by Jason Szep and Tom Brown in Florida; Editing by David Wiessler)