CHARLESTON, S.C. — Senator McCain today called the Democratic contest “still very competitive” but said his South Carolina win gives him momentum heading into the next big battle in Florida. The Arizona senator and Senator Clinton won contentious nominating contests a day earlier.

Mr. McCain took a swipe at Mayor Giuliani, who avoided the early primary states to make his first big stand in Florida, which votes January 29. Mr. McCain said he expected to come under heavy criticism from the former New York mayor.

“If someone hasn’t run a primary, I can understand why they would attack the front-runner,” Mr. McCain told reporters at a news conference.

Mr. McCain clearly was buoyed by the victory, his second this season after winning the New Hampshire primary earlier this month. In 2000, Mr. McCain was defeated in South Carolina by George W. Bush, a loss that effectively ended that campaign.

“Right now, we’re enjoying the win,” he said.

As to his come-from-behind rise in the Republican ranks, Mr. McCain said, “I certainly enjoy being the underdog. I much more enjoy being ahead.”

“I think we’re obviously doing very well,” Mr. McCain said. Still, he added, “This is still very competitive.”

Attention in the race for the Republican presidential nomination shifts to Florida, where Mr. Giuliani has held court for weeks, and to Mr. McCain.

Mr. Romney today portrayed himself as a Washington outsider compared to Mr. McCain, who Mr. Romney said has been “in Washington all his life.” Mr. Romney, appearing on “Fox News Sunday,” said the campaign is about who is best suited to change Washington and “I just don’t think that somebody who has spent their life inside Washington, who has lobbyists on every elbow … I just don’t think that’s going to get Washington fixed.”

Mr. Giuliani said he was ready for his rivals to come on down.

“Florida is a microcosm of the country. It’s a diverse state, reflects America,” he said on ABC’s “This Week.” “It determined our president in 2000,” Mr. Giuliani, who has watched his lead in national polls shrink while other states voted and he hung out in the Sunshine State, said.

Asked about Mr. McCain, Mr. Giuliani said: “The case for me is that I am the strongest fiscal conservative.” He noted that Mr. McCain voted against President Bush’s tax cuts. Mr. Giuliani also said he has “executive experience others haven’t had.”

Mr. McCain bested a former Arkansas governor, Michael Huckabee, in a South Carolina fight that focused on the economy.

“Thank you, my friends, and thank you, South Carolina, for bringing us across the finish line first in the first-in-the-South primary. It took us a while. But what’s eight years among friends,” Mr. McCain told a boisterous crowd of supporters at a victory rally last night.

Attention turns to Florida’s contest on January 29, followed by voting in 22 states on February 5.

On the Democratic side, Mrs. Clinton defeated Senator Obama in a tight Nevada contest.

Among Republicans, a former Massachusetts governor, Mitt Romney, cruised to victory in the little-contested Republican Nevada caucuses.

But Mr. McCain’s victory in South Carolina could shake up the Republican contest and give him political grasp. Mr. McCain won in New Hampshire, then placed second to Mr. Romney in Michigan.

“We’ve got a long way to go,” Mr. McCain said yesterday. The man whose campaign was left for dead six months ago predicted that victory in the first Southern primary would help him in the coming contests.

Mrs. Clinton claimed the Nevada vote as a victory. “This is one step on a long journey,” Mrs. Clinton told cheering supporters in Las Vegas. She captured the popular vote, but Mr. Obama edged her out for national convention delegates at stake, taking 13 to her 12.

Mr. Obama issued a statement that said he had conducted an “honest, uplifting campaign … that appealed to people’s hopes instead of their fears.”