GREENVILLE, S.C. — Donald Trump and Jeb Bush traded shots in a biting and personal fight over the legacy of President George W. Bush during the Republican debate here on Saturday night, after Trump asserted the former president irresponsibly led the country to war in Iraq and failed to prevent the attacks on Sept. 11, 2001.

The debate was rollicking and at times out of control, with tempers high in front of a feisty crowd. The candidates fought to notch game-changing performances before South Carolina primary voters cast ballots Feb. 20.

Going after George W. Bush posed risks for Trump in a state where the 43rd president remains enormously popular, with approval ratings above 80 percent. The crowd repeatedly booed Trump, who spoke into the cameras and suggested that the live audience was packed with donors and lobbyists.

“Obviously the war in Iraq was a big fat mistake,’’ Trump said. “We can make mistakes. But that one was a beauty. We should have never been in Iraq.’’

Standing on the debate stage, Trump made arguments familiar to liberal Democrats who loathe the war. “They lied!’’ Trump said. “They said there were weapons of mass destruction. There were none, and they knew there were none.’’

Bush rose to the challenge more aggressively than he has in previous debates when he or his family was attacked by Trump.

“I [couldn't] care less about the insults that Donald Trump gives to me. It’s bloodsport for him, he enjoys it, and I’m glad he’s happy about it,’’ he said. “But I am sick and tired of him going after my family.’’

Then, speaking to an audience friendly to the Bush clan, he added: “While Donald Trump was building a TV show, my brother was building the apparatus to keep us safe, and I’m glad he did.’’

Trump interjected.

“The World Trade Center came down during your brother’s reign. Remember that,’’ he said, adding he lost “hundreds of friends’’ in the attacks.

Bush got in several other jabs at Trump. “This is a guy who gets his foreign policy from the shows,’’ Bush said. “This is a guy who insults his way to the nomination.’’

“He has had the gall to go after my mother,’’ he added. “My mom is the strongest woman I know.’’

“She should be running,’’ Trump responded.

With tempers flaring, Ohio Governor John Kasich seemed aghast.

“This is just crazy,’’ he said. “This is just nuts. Jeez. Oh, man.’’

The debate was the first time the candidates met face-to-face after the New Hampshire primary, where Trump easily defeated the rest of the field and left a muddled picture in the battle for second place.

Now that the primary campaign has reached South Carolina, a state known for its gritty political culture, Trump’s rivals, especially Bush and Cruz, have launched increasingly strident attacks to prevent him from steamrolling to the nomination.

The two-hour debate, sponsored by CBS News and the Wall Street Journal, was the ninth meeting of the candidates on stage, with the pack now winnowed to six. The debate was held at the Peace Center, an ironic venue given the tenor of the discussion.

Cruz and Marco Rubio displayed deep disdain for one another on immigration. Trump told Cruz, over and over, he was “a liar’’ who has no friends in the Senate.

“You are the single biggest liar,’’ Trump shot at Cruz. “You are probably even worse than Jeb Bush...This guy will say anything. Nasty guy.’’

The debate Saturday night was the first opportunity for Rubio to make good on a promise to perform better. The Florida senator botched the previous debate in New Hampshire, a dismal performance that he conceded led to his fifth-place finish in the primary.

Kasich, who is trying to capitalize on his second-place finish in New Hampshire, refrained from throwing punches.

“I don’t want to get in this fighting,’’ he said. “I’m going to stay positive about what I want to do.’’

Cruz attacked Rubio over immigration on Saturday night, citing comments he made in Spanish to the station Univision.

“I don’t know how he knows what I said on Univision because he doesn’t speak Spanish,’’ Rubio said. Cruz then began speaking in Spanish.

Matt Viser can be reached at matt.viser@globe.com. Follow him on Twitter @mviser.