After splitting wins in weekend balloting, top GOP presidential candidates Donald Trump and Sen. Ted Cruz are focusing on big upcoming primaries, particularly in Florida where they hope to finish off rival Sen. Marco Rubio in his home state.

On Sunday, Rubio won the Puerto Rico Republican primary in which 23 delegates are up for grabs. But the GOP field is already looking toward the March 15 primaries -- including ones in Ohio and Florida.

The front-running Trump and Cruz, now firmly in second place in the GOP race, have called for Rubio to exit the contest, after losing in all five states Saturday and winning only Minnesota, and now Puerto Rico.

“I would like to face Ted. I would prefer it,” Trump told Fox News on Sunday, when asked about his call for Rubio to exit.

The billionaire businessman argued that he could do better toward winning the nomination by facing the Texas senator alone in such upcoming primaries as New York, New Jersey and California.

“I want Ted one-on-one,” Trump said Saturday night in Florida after winning the Kentucky caucus and Louisiana primary. Cruz won the GOP caucuses in Kansas and Maine.

Cruz has suggested since the Super Tuesday primaries last week that rivals -- including Rubio and Ohio Gov. John Kasich, now the only other GOP candidate -- should drop out so Republican voters can coalesce around an establishment candidate and stop Trump’s march to the nomination.

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

In a clear effort to at least keep Rubio from winning his home state, Cruz has now opened 10 campaign offices in Florida.

And Trump, who has popular golf resorts in the state and an appeal to retiree voters from the Northeast, also is aiming for a top finish.

Rubio said Saturday’s races were not ones in which he expected to do well, but has repeatedly said he will win Florida.

The senator told Fox News after his disappointing Super Tuesday finish that he won’t quit if he loses Florida and will “campaign in all 50 states, even if I have to get in my pickup truck and drive all over this country.”

Kasich has also insisted he’ll win his home state on March 15, with polls showing him in a tight race with Trump.

“Just watch, we have a lot of momentum,” he told ABC’s “This Week.” “Since the debate [Thursday] we are closing the gap.”

Trump leads the field in Michigan, which votes Tuesday, by about 10 percentage points, according to most polls. The state has 59 GOP delegates up for grabs.

Ohio has 66 and Florida has 99, in winner-take-all GOP contests.

The total GOP delegate count now is 378 for Trump, 295 for Cruz, 123 for Rubio and 34 for Kasich, with 1,237 needed to win the party’s presidential nomination.

 “We had a pretty good night,” Trump also told Fox News on Sunday, acknowledging that he didn’t spend a lot of time campaigning in Maine.

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

Despite the support of many elected officials, Rubio finished in third place in every state that voted Saturday except Maine, where The Associated Press projected him to finish behind Kasich.

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

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.

GOP 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, Fla. At the rally, the billionaire businessman had supporters raise their hands and swear to vote for him.

The Associated Press contributed to this report.