Donald Trump and Ted Cruz urge each other to go
It is fresh evidence that there is no quick end in sight to the bitter contest, and both men suggested other rivals should now quit.
On the Democratic side, Bernie Sanders won in Nebraska and Kansas, while frontrunner Hillary Clinton took Louisiana, another divided verdict from the American people.
Cruz, a Texas senator, claimed Kansas and Maine, and declared it “a manifestation of a real shift in momentum”.
Billionaire Trump, still the frontrunner in the hunt for delegates, took Louisiana and Kentucky.
In the overall race for Republican delegates, Trump led with at least 375 and Cruz had at least 291. Marco Rubio had 123 delegates and John Kasich had 33. It takes 1,237 delegates to win the Republican nomination for president.
Clinton had at least 1,117 delegates to Mr Sanders’ 477, including superdelegates — members of Congress, governors and party officials who can support the candidate of their choice.
It takes 2,383 delegates to win the Democratic nomination, and there were 109 at stake on Saturday.
Establishment figures are looking frantically 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 former nominees Mitt Romney (2012) and Senator John McCain (2008) — are fearful a Trump victory would lead to losses up and down the Republican ticket in Novemebr.
“Everyone’s trying to figure out how to stop Trump,” the real estate tycoon marvelled at a rally in Orlando, Florida, where he had supporters raise their hands and swear to vote for him.
Cruz suggested it was time for other Republican candidates to quit the race so that he could go one-on-one with Mr Trump. Trump said it was “probably time” for Rubio to drop out, after he finished no better than third in any of the four states.
In Maine, Cruz won by a comfortable margin.
On the Democratic side, meanwhile, Sanders won by a solid margin in Nebraska, and Kansas gave him a seventh victory so far in the nominating season.
Clinton, who has been doing well with African-American voters, had an easy win in Louisiana.
It was anger that propelled many of Trump’s voters to the polls. “It’s my opportunity to revolt,” said Betty Nixon, a 60-year-old Trump voter in Olathe, Kansas. She said she liked the businessman because “he’s not bought and paid for”.
Overall, Trump had prevailed in 10 of 15 contests heading into Saturday’s voting. Rubio had one win in Minnesota.
Rubio and Ohio governor John Kasich both pinned their hopes on winner-take-all contests on March 15 in their home states.
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