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Republican Senator Ted Cruz has managed to check the ascent of presidential rival Donald Trump towards winning the candidacy in another day of primaries, in which Democratic candidate Bernie Sanders secured two victories and his rival, Hillary Clinton, cemented her hold in the South with a win in Louisiana.

Cruz prevailed over Trump in the Kansas and Maine caucuses while the business magnate won in Kentucky and Louisiana.

On the Democratic front, Sanders won the Kansas and Nebraska caucuses, continuing his good run in the Midwest, while Clinton won in Louisiana.

To a Republican party faced with the prospect that Trump could win the candidacy in the July convention, Cruz's twin victories were probably bittersweet.

The ultra-conservative Texas senator, despised by the traditional section of the party, has claimed to be the only viable alternative to Trump, but it remains to be seen if he gains the acceptance of the Republican elites, who have backed his rival Marco Rubio so far.

"After tonight, we have seen that our campaign is the only campaign that has beaten, that can beat, and that will beat Donald Trump," Cruz said at a press conference in Boise, Idaho, after announcing his wins, which puts his tally at seven against 12 for Trump.

"For the candidates who have not yet won a state, who have not racked up significant delegates: I ask you to prayerfully consider our coming together," he added.

Of the other two Republican hopefuls, Marco Rubio has only won Minnesota, while Ohio Governor John Kasich has yet to secure a single win.

Trump was more forthcoming in asking Rubio to drop out of the presidential nomination race.

"I think Marco Rubio had a very, very bad night and personally I call for him to drop out of the race," Trump said of the Florida senator at a press conference in West Palm Beach, Florida.

"I would love to take on Ted one-on-one," said the magnate, adding: "That would be so much fun, because Ted can't win New York. He can't win New Jersey. He can't win Pennsylvania. He can't win California."

Meanwhile, the Democrats did not focus on the three states voted on Saturday but on Michigan, which will hold its primary on Tuesday and is considered by both candidates as important to strengthen their respective campaigns.

With victories in Nebraska and Kansas, the last by a wide margin, Sanders has won in seven states and has 432 lawmakers against 1,066 for Clinton, who has the overwhelming support of "superdelegates" or elected Democratic officials who can cast their votes at the convention.

The 74-year-old independent senator's strategy is to continue his campaign until June when the delegate-rich California holds its primary, picking up wins along the way.

Clinton once again solidified her hold on the South with a win in Louisiana, which offset losses in Kansas and Nebraska in terms of delegates.

"I am thrilled we are adding to our pledged delegate count. I'm grateful to everyone who turned up to support us. But now all eyes turn to Michigan," said Clinton, favorite to win in that state, at a rally in Detroit.