By Steve Holland

CHARLESTON, South Carolina (Reuters) - Republican presidential candidate John McCain predicted on Sunday he would do well in the Florida primary election this month after winning South Carolina and took a swipe at rival Rudy Giuliani.

McCain, buoyant after winning on Saturday in the first contest in the U.S. South as voters choose candidates for the November presidential election, said he expected to get a boost of momentum from the victory.

"I still think this is very competitive," the Arizona senator said at a news conference.

"I think we are doing very well. I think Florida is very important. I don't know if it's a must-win but it's certainly a very, very important race," he said.

McCain was headed to Miami to begin a weeklong sprint of campaign appearances across much of Florida. Giuliani, a former mayor of New York, and former Massachusetts Gov. Mitt Romney were already in Florida for its January 29 vote, to be followed soon by contests in 22 states on February 5, when the nominee may emerge.

In the wake of McCain's South Carolina victory, Giuliani adviser Tony Carbonetti issued a statement calling attention to McCain's vote against President George W. Bush's tax cuts.

McCain was dismissive when asked to respond. Giuliani has not competed heavily in the main early voting states of Iowa, New Hampshire and South Carolina, preferring to wait until Florida to see if he can score a breakthrough in a large state with a large population of retired New Yorkers.

Polls in Florida show a tight race in which McCain leads Giuliani and Romney.