Republican Senator Ted Cruz won in Kansas and Maine, while New York billionaire Donald Trump compensated by snatching a victory in Louisiana and Kentucky.
During his speech on Saturday, Trump ridiculed Rubio’s recent losses, calling on him to drop out of the race.
“Marco Rubio had a very, very bad night and personally I’d call for him to drop out of the race,” he said. “I think it’s probably time.”
“As a party we should come together and stop this foolishness,” he added later.
Cruz said the results showed he was gaining momentum in the race to catch Trump.
"The scream you hear, the howl that comes from Washington, D.C., is utter terror at what 'We the People' are doing together," Cruz told supporters in Coeur d'Alene, Idaho, after his win in Kansas.
Saturday’s caucuses were not good for Republican Senator Marco Rubio of Florida and Ohio Governor John Kasich as both shut out in the day's four Republican contests.
The races were open only to registered Republicans, but not the independent and disaffected Democratic voters who have helped Trump to be the front-runner candidate.
On the Democratic side, Vermont Senator Bernie Sanders recorded two crucial victories in Kansas and Nebraska as he tries to narrow the gap with the overall front-runner Hillary Clinton, who won in Louisiana.
Following his wins on Saturday, Sanders said he was not planning to end his efforts for the White House anytime soon.