David Jackson

USA TODAY

COLUMBIA, S.C. — Donald Trump easily won the South Carolina primary on Saturday, taking another major step toward the Republican presidential nomination while Marco Rubio edged out Ted Cruz in a tight battle for second place.

"Let's put this thing away, and let's make America great again!" Trump told cheering supporters in Spartanburg, S.C., as he predicted further success in upcoming states like Nevada, Georgia, and Texas.

The New York billionaire said he is leading "an incredible movement with incredible people," as the crowd chanted "U-S-A! U-S-A!"

Former Florida governor Jeb Bush, meanwhile, announced he would suspend his presidential campaign in the wake of what looked like a single-digit finish in the Palmetto State, "The people of Iowa and New Hampshire and South Carolina have spoken, and I really respect their decision," said Bush, who had poor finishes in all three states.

John Kasich and Ben Carson were also well behind in South Carolina, raising questions about the long-term prospects of their campaigns, though both indicated they have no plans to withdraw from the race.

Rubio and Cruz, meanwhile, sharpened their battle to be the alternative to Trump, who faces heavy opposition from many traditional Republicans. They fear the brash billionaire may not be able to win the general election and could drag down other GOP candidates.

"After tonight, this has become a three-person race, and we will win the nomination," Rubio told cheering backers in Columbia, S.C.

Cruz, also speaking in Columbia, said he is the only true conservative "who can beat Donald Trump," noting that he turned the trick in Iowa. "Conservatives continue to unite behind our campaign," said the Texas senator who has questioned Rubio's commitment to the cause.

Trump, whose South Carolina campaign included attacks on former Republican president George W. Bush over the Iraq war and a flap with Pope Francis over immigration, did well with new GOP voters who are angry at the government and want major change.

An easy winner of the New Hampshire primary on Feb. 9, Trump told South Carolina crowds throughout the week that a win Saturday would enable him to "run the table" in future primaries and caucuses en route to the Republican presidential nomination.

All the candidates are preparing for those future contests, including caucuses Tuesday in Nevada, and a string of Southern primaries on March 1.

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Trump says he could 'run the table' if he wins South Carolina

Cruz, who defeated Trump in the Iowa caucuses and was hoping for a repeat in the first Southern primary, says he is seeking to build "the old Reagan coalition" of evangelicals, economic conservatives, young people and Ronald Reagan-style Democrats.

While Cruz argued during the campaign in South Carolina that Trump is a fake conservative who has backed Democratic causes in the past, Trump accused Cruz of being a liar and dirty trickster. Trump even threatened to file a lawsuit challenging Cruz's eligibility to be president because he was born in Canada. Cruz invited the lawsuit, saying he looked forward to deposing Trump (and that he is eligible under the natural-born citizen provision of the Constitution because his mother was a U.S. citizen).

Trump, whose comments about Mexican immigrants, women, and critics in general have been condemned throughout the campaign, added more controversial statements to that list during his time in South Carolina.

During his North Charleston appearance, Trump told an apocryphal story about a U.S. general — John J. Pershing — who executed accused Islamic terrorists a century ago with bullets dipped in pigs' blood. Historians have debunked the tale.

Rubio, the Florida senator, called Trump's tale "bizarre," and told NBC's Weekend Today show that "I’m sure people are offended. We hope people are offended by that. That’s not what the United States is about.”

After finishing a disappointing fifth place in New Hampshire, Rubio campaigned in South Carolina with the help of endorsements from prominent state lawmakers, including Gov. Nikki Haley and Sen. Tim Scott.

Seeking a one-on-one showdown with Trump or Cruz down the line, Rubio told Fox News that "we feel really good about this race when it narrows down."

Rubio to S.C. voters: 'This election is a generational choice'

The South Carolina campaign also signaled the end of the Bush political dynasty. Jeb Bush, the son and brother of previous presidents, continued to face attacks from Trump and had more trouble connecting with voters. During one town hall this week, voters peppered Bush with questions about his campaign, drawing a frustrated response from the candidate.

Kasich, the Ohio governor who finished second to Trump in New Hampshire, had acknowledged his underdog status in South Carolina, and is already looking toward future primaries and caucuses. Kasich was not even in South Carolina on Saturday, appearing instead at events in Vermont and Massachusetts, states that also hold contests on March 1.

As the South Carolina returns rolled in, Kasich campaign manager John Weaver tweeted that his candidate has no plans to pull out of the race: "The nomination battle is down to Final Four, with @JohnKasich headed to favorable states. Only Gov & clear path. No more being out spent!"

Carson, the retired neurosurgeon who seemed headed for a sixth-place finish in South Carolina, told supporters he has no plans to withdraw: "We still have the ability to dictate the course of our country -- we still have the ability to save it for the next generation."

Elections 2016 | USA TODAY Network

Voters in South Carolina offered a variety of reasons for their choices Saturday. Taylor Hall, a 23-year-old law student at the Charleston School of Law, said he planned to vote Trump because “it's time for a wake up call in this country."

Despite a handshake from Bush at his polling place on Daniel Island, near Charleston, mechanical engineer Ray Summerow, 25, said he went with Cruz. Summerow said that while Trump has taken liberal positions in the past, the Texas senator has been more of a consistent conservative.

Harold Turner, 87, who cast his first presidential vote for Barry Goldwater in 1964, said he decided to back Rubio this year after seeing him speak in Charleston.

“He was truthful, comfortable," he said. "Not being argumentative.”

More voters, however, went for Trump.

Tyler Westbrook, 53, a retired stock analyst from Charleston, said he simply doesn’t like the direction the country is going in.

“I think it’s time for a big change,” Westbrook said, “and obviously you know who I’m voting for if I’m in the Republican primary wanting change — it’s got to be Mr. Trump.”

Contributing: Julia Jacobs, Nicolas Rivero and Shane McKeon, Medill News Service