(AP) -- Republican Donald Trump and Democrat Hillary Clinton swept through the South on Super Tuesday, claiming victory in their parties' primaries in delegate-rich Georgia, Tennessee, Alabama and Virginia. The front-runners appeared ever more likely to end up in a general election showdown.

On the Republican side, Ted Cruz won his home state of Texas, the night's single biggest prize, as well as neighboring Oklahoma. Democrat Bernie Sanders picked up his home state of Vermont, as well as Oklahoma, Colorado and Minnesota, but failed to broaden his appeal with minority voters who are crucial to the party in presidential elections.

The night belonged to Trump and Clinton, who turned the busiest day of the 2016 primaries into a showcase of their strength with a wide swath of American voters.

Signaling her confidence, Clinton set her sights on Trump as she addressed supporters during a victory rally.

"It's clear tonight that the stakes in this election have never been higher and the rhetoric we're hearing on the other side has never been lower," she said.

Trump, too, had his eye on a general election match-up with the former secretary of state, casting her as part of a political establishment that has failed Americans.

"She's been there for so long," Trump said at his swanky Mar-a-Lago resort in Florida. "If she hasn't straightened it out by now, she's not going to straighten it out in the next four years."

Trump's dominance has rattled Republican leaders, who fear he's unelectable against Clinton in November. Even as Trump professed to have good relationships with his party's elite, he issued a warning to House Speaker Paul Ryan, who declared earlier in the day that "this party does not prey on people's prejudices." Trump said that if the two don't get along, "he's going to have to pay a big price."

But all efforts to stop Trump have failed, including an aggressive campaign by Florida Sen. Marco Rubio to discredit the billionaire businessman.

For Rubio, Super Tuesday turned into a bitter disappointment. He emerged with his first victory in Minnesota but failed to live up to the wider hopes of the numerous Republican officeholders who have promoted him as the party's best alternative to Trump.

With an eye on Florida's March 15 primary, Rubio vowed to keep up efforts to "unmask the true nature of the front-runner in this race."

Cruz desperately needed his win in Texas in order to stay in the race. He's the only Republican to beat Trump this primary season, a fact he wielded as he called on Rubio and other candidates to step aside.

"I ask you to prayerfully consider our coming together, united," Cruz said.

With results still coming in, Trump had won at least 139 Super Tuesday delegates, while Cruz picked up at least 52. Overall, Trump leads the Republican field with 221.

Sanders' wins did little to help him make up ground in his delegate race with Clinton. She was assured of winning at least 334 of the 865 at stake on Super Tuesday. That's compared to Sanders, who had at least 145 delegates.

Clinton also picked up wins in Arkansas, and Texas, while Trump carried the GOP contests in Arkansas and Massachusetts.

Trump's wins in the South were a major blow to Cruz, who once saw the region as his opportunity to stake a claim to the nomination. Instead, he's watched Trump, a brash New York real estate mogul, display surprising strength with evangelical Christians and social conservatives.

Republicans spent months largely letting Trump go unchallenged, wrongly assuming his populist appeal would fizzle. Instead, he's appeared to grow stronger, drawing broad support for some of his most controversial proposals.

In six of the states on Tuesday, large majorities of Republican voters said they supported a proposal to temporarily ban all non-citizen Muslims from entering the United States, an idea championed by Trump. Nine in 10 of Trump's voters were looking for an outsider, and half were angry with the government, according to exit polls conducted by Edison Research for The Associated Press and television networks.

In the Democratic race, Clinton has steadied herself after an unexpectedly strong early challenge from Sanders. The Vermont senator did carry his home state decisively, and told the crowd at a raucous victory party that he was "so proud to bring Vermont values all across this country."

Sanders, who has energized supporters with his calls for a "political revolution," has struggled to expand his base beyond young people and liberals. His weakness with black voters, a core part of the Democratic constituency, was underscored anew.

Clinton was supported by at least 80 percent of black voters in Alabama, Arkansas, Virginia, Georgia, Tennessee and Texas. She was also bolstered by women and older voters.

More than 90 percent of Clinton's voters wanted an insider, according to exit polls, and nearly half said experience was the top quality they were looking for in a candidate.