Donald Trump renewed calls Saturday night for Florida Sen. Marco Rubio to drop out of the Republican race, saying he wants to take on Texas Sen. Ted Cruz in a two-man GOP showdown for the 2016 party nomination.

“Marco has to get out of the race. He has to,” Trump said.  “Man, do I want to run against just Ted.”

Trump and Cruz were Saturday’s big winners, claiming two victories each in four Republican state contests. Trump won the Kentucky caucus and Louisiana primary while Cruz claimed caucus wins in Kansas and Maine.

Cruz attributed his strong showing to conservatives coalescing behind his candidacy, calling it “a manifestation of a real shift in momentum.”

He suggested it was time for Rubio and Ohio Gov. John Kasich to call it quits.

“As long as the field remains divided, it gives Donald an advantage,” Cruz said.

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Despite the support of many elected officials, Rubio’s lackluster performance Saturday raises serious questions about his viability in the race. He finished in third place in every state that voted Saturday except Maine, where The Associated Press projected him to finish behind Kasich.

Rubio said the upcoming schedule of primaries would be "better for us," and renewed his vow to win his home state of Florida, claiming all 99 delegates there on March 15.

Saturday’s races saw high voter turnout in several states. Turnout in Republican presidential caucuses in Kansas exceeded the party's most optimistic predictions.

State GOP Executive Director Clay Barker said at least 73,000 people cast ballots in Saturday's caucuses. He said there are another 6,000 provisional ballots and 1,000 absentee ballots sent to voters but not yet collected.

That compares to about 30,000 people voting in the state's GOP caucuses in 2012 and about 20,000 voting in 2008.

The party had 60,000 ballots printed this year and then warned caucus sites to be prepared to print more.

With the GOP race in chaos, establishment figures are looking for any way to derail Trump, perhaps at a contested convention if no candidate can get enough delegates to lock up the nomination in advance.

Party leaders -- including 2012 nominee Mitt Romney and 2008 nominee Sen. John McCain -- are fearful a Trump victory would lead to a disastrous November election, with losses up and down the GOP ticket.

"Everyone's trying to figure out how to stop Trump," Trump marveled about himself at an afternoon rally in Orlando, Florida. At the rally, the billionaire businessman had supporters raise their hands and swear to vote for him.

On the Democratic side, there was another divided verdict from voters. Vermont Sen. Bernie Sanders notched wins in the Nebraska and Kansas caucuses, while front-runner Hillary Clinton snagged a win in the Louisiana primary.

"No matter who wins this Democratic nomination, I have not the slightest doubt that on our worst day we will be infinitely better than the Republicans on their best day,” Clinton said.  

She also said she was thrilled to add to her delegate count and expected to do well in Michigan’s primary on Tuesday. But before that, she and Sanders will go head-to-head Sunday in Maine’s Democratic caucus where 30 delegates are up for grabs. Republicans will battle it out in Puerto Rico’s GOP caucus for 23 delegates.

Despite Clinton’s commanding lead in the delegate count, Sanders vowed to keep fighting until the Democratic convention in Philadelphia this summer.  

The Associated Press contributed to this report.