Washington (CNN) Donald Trump and Ted Cruz claimed two Super Saturday victories each while Democrat Bernie Sanders also scored a pair of morale-boosting wins and Hillary Clinton won one state.

The campaign now moves to Michigan, which holds its primary on Tuesday along with races in three other states. But the wins by Trump and Cruz on Saturday guarantee they will continue their battle for the Republican nomination at least through March 15, when major states including Florida and Ohio go to the polls.

"I have been in competitions all of my life," Trump said in a press conference at Trump International Golf Course in West Palm Beach, Florida. "There is nothing so exciting as this stuff."

Sanders won Kansas and Nebraska while Clinton won the night's big prize: delegate-rich Louisiana. They will face off Sunday night at CNN's Democratic debate in Flint, Michigan.

On the Republican side, Trump won Louisiana and Kentucky while Cruz won Kansas and Maine.

The Texas senator's strong night represents a rebound from Super Tuesday contests last week, when his hoped-for lock on Southern, conservative states failed to materialize and cast doubts on the resilience of his appeal to Republican voters. It also validates a growing theme that he performs best in races with closed primaries and caucuses, contests in which only registered Republicans can participate.

"God bless Kansas. And God bless Maine," Cruz said, and argued that his performance on Saturday represented an important pivot point in the GOP race. "What we are seeing is Kansas is a manifestation of a real shift in momentum."

Photos: Who's running for president? Photos: Who's running for president? Ted Cruz, Donald Trump, John Kasich, Hillary Clinton and Bernie Sanders, Hide Caption 1 of 6 Photos: Who's running for president?



"So, ladies and gentlemen, I am officially running for president of the United States, and we are going to make our country great again," Trump told the crowd at his announcement. Businessman Donald Trump announced June 16 at his Trump Tower in New York City that he is seeking the Republican presidential nomination. This ends more than two decades of flirting with the idea of running for the White House."So, ladies and gentlemen, I am officially running for president of the United States, and we are going to make our country great again," Trump told the crowd at his announcement. Hide Caption 2 of 6 Photos: Who's running for president?



"These are all of our stories," Cruz told the audience at Liberty University in Virginia. "These are who we are as Americans. And yet for so many Americans, the promise of America seems more and more distant." Sen. Ted Cruz of Texas has made a name for himself in the Senate, solidifying his brand as a conservative firebrand willing to take on the GOP's establishment. He announced he was seeking the Republican presidential nomination in a speech on March 23."These are all of our stories," Cruz told the audience at Liberty University in Virginia. "These are who we are as Americans. And yet for so many Americans, the promise of America seems more and more distant." Hide Caption 3 of 6 Photos: Who's running for president? Ohio Gov. John Kasich joined the Republican field July 21 as he formally announced his White House bid.



"I am here to ask you for your prayers, for your support ... because I have decided to run for president of the United States," Kasich told his kickoff rally at the Ohio State University. Hide Caption 4 of 6 Photos: Who's running for president?



"Everyday Americans need a champion, and I want to be that champion -- so you can do more than just get by -- you can get ahead. And stay ahead," she said in her announcement video. "Because when families are strong, America is strong. So I'm hitting the road to earn your vote, because it's your time. And I hope you'll join me on this journey." Hillary Clinton launched her presidential bid on April 12 through a video message on social media. The former first lady, senator and secretary of state is considered the front-runner among possible Democratic candidates."Everyday Americans need a champion, and I want to be that champion -- so you can do more than just get by -- you can get ahead. And stay ahead," she said in her announcement video. "Because when families are strong, America is strong. So I'm hitting the road to earn your vote, because it's your time. And I hope you'll join me on this journey." Hide Caption 5 of 6 Photos: Who's running for president?



"This great nation and its government belong to all of the people and not to a handful of billionaires, their super PACs and their lobbyists," Sanders said at a rally in Vermont on May 26. Sen. Bernie Sanders , an independent from Vermont who caucuses with Democrats, announced his run in an email to supporters on April 30. He has said the United States needs a "political revolution" of working-class Americans to take back control of the government from billionaires."This great nation and its government belong to all of the people and not to a handful of billionaires, their super PACs and their lobbyists," Sanders said at a rally in Vermont on May 26. Hide Caption 6 of 6

Trump lobbed criticism at his GOP rivals. He said Rubio had a "very, very bad night" and called on him to drop out of the race. And he took at shot at Cruz, after spending months saying the Texas senator is ineligible to run for President because he was born in Canada.

"He should do well in Maine because it is very close to Canada," Trump said.

Tough night for Rubio

It was another grim night for Rubio, who has so far won only one of the 19 contests in the GOP race, despite billing himself as the only candidate with the potential to unify the Republican Party and the broad appeal needed to beat Clinton.

While Kansas and Maine may represent too small a sample to validate Cruz's claims that the race is now a two-man affair, it is clear that his win will be parsed for signs that it represents the stirrings of a backlash against Trump, after the billionaire became embroiled in a controversy he was slow to repudiate the Ku Klux Klan, and introduced a vulgar note into a Republican debate on Thursday night.

On the other hand, the victory by Cruz in Kansas appears to fit squarely into historical precedent. Like Cruz, the previous two victors of that state's GOP contests, Rick Santorum in 2012 and Mike Huckabee in 2008, had strong appeal among evangelicals which they had also demonstrated by winning the Iowa caucuses.

Neither went on to win the nomination.

And despite his win Saturday in Maine and on Tuesday in Alaska, there are still doubts about whether Cruz can expand his appeal beyond hard-core conservatives in a national race.

Super Saturday voting took place in the wake of former Republican nominee Mitt Romney's assault on Trump, which ignited a civil war within the GOP between establishment figures and the billionaire's army of angry 'outsider' voters.

Democratic race

Sanders' wins in the Kansas and Nebraska — both caucus states — could offer him a boost after he was overshadowed by Clinton on Super Tuesday. But they also appear to underline that Sanders is stronger among largely white, less diverse electorates. That is a problem for Sanders because the nomination could be decided by the large numbers of minority voters in the Democratic coalition, to which Clinton has demonstrated she has more appeal.

Clinton's campaign also worked in both states to narrow the margin of her defeat, learning the lessons from the 2008 campaign when Barack Obama piled up large delegate counts in caucus states. The manageable size of her defeats in the two states and her big win in Louisiana will mean that she will likely end the night slightly further ahead of Sanders in the overall delegate count than when she started it.

The Super Saturday contests offer a chance for the two front-runners to quicken their momentum after they both came out of the contests last Tuesday with solid delegate leads. They still face major battles in crucial elections in Michigan, Ohio and Florida over the coming weeks.

Clinton has a lead of about 200 pledged delegates over Sanders, while Trump leads Cruz by around 100 delegates and is about 200 delegates ahead of the third place candidate Rubio.

Rubio put on a brave face, saying that the states being contested on Super Saturday favored other candidates, but predicted that his fortunes would soon change. He predicted victory in his home state of Florida on March 15.

"The map only gets friendlier for us after tonight," Rubio told reporters during a trip to Puerto Rico, which holds a Republican primary on Sunday. "There will be more delegates awarded in Florida than basically every state that voted tonight combined."