Super Tuesday could be summed up this way: It delivered clear victories for the front-runners and slivers of hope for the losers.

The biggest day thus far in the US presidential campaign saw Hillary Clinton, the Democratic favourite, and Donald Trump, the leading Republican, make big strides toward their goal of becoming their party's nominee to run for president in November's general election.

But their rivals performed well enough to postpone tough decisions about any of them leaving the race, at least until after the primaries in other large states later in March.

Clinton, a former secretary of state, won Texas, Tennessee, Virginia, Georgia, Alabama, Massachusetts and Arkansas - seven of the 11 states that voted on the Democratic side. But she had to concede Colorado, Vermont, Oklahoma and Minnesota to her more liberal challenger, Bernie Sanders, who says he wants a "political revolution."

Still, Clinton piled up many more delegates because she won by larger margins in big states. But to the victor go not all the spoils. Both parties divide delegates proportionally based on the number of votes received in Super Tuesday states.

Trump, the most controversial major candidate in modern US presidential politics, chalked up victories in seven states: Georgia, Alabama, Massachusetts, Virginia, Tennessee, Arkansas and Vermont. But he lost the important state of Texas - the one with the most delegates up for grabs Tuesday - to arch-conservative Ted Cruz.

Democrats in Texas chose a total of 252 delegates, and the Republicans 155. Cruz was expected to win the state, which he represents in the US Senate. He also edged out Trump in Oklahoma, while Florida Senator Marco Rubio won Minnesota. Cruz and Rubio finished with more delegates together than Trump received Tuesday, though the billionaire has an overall lead in the count.

Cruz also finished second in four states, prompting him to call for the field of Republican candidates, which in addition to Rubio includes Ohio Governor John Kasich and retired neurosurgeon Ben Carson, to rally behind him.

"Our campaign is the only campaign that has beaten, that can beat and that will beat Donald Trump," Cruz said.

As long as there are five candidates, a nomination for Trump is more likely, the evangelical Christian said, adding: "I ask you to prayerfully consider our coming together, uniting."

About 20 per cent of all delegates were decided on Super Tuesday: a total of 600 among the Republicans and about 1,000 among the Democrats. A Republican candidate needs 1,237 delegates to win the nomination and a Democrat needs 2,383.

Sanders put up a hard fight in a few states against the former US senator from New York and former first lady. He won Vermont, his home state, Oklahoma, Minnesota and Colorado. Massachusetts was won by Clinton - barely. Sanders won New Hampshire last month.

"All across our country today they - Democrats - voted to break down barriers so we can all rise together," Clinton said.

"America is strong when we're all strong. America never stopped being great," she said, rebuking Trump's campaign slogan, "Make America great again."

Trump didn't hold a victory rally, but took the opportunity to answer questions from reporters at a swanky venue he owns in the wealthy Florida city of Palm Beach. He said he would be a "unifier" and would work to get to know leaders in Congress.

He was introduced by New Jersey Governor Chris Christie, who recently endorsed Trump in a surprising move. Christie praised Trump as a "tough," "strong" and "bold."

But in fact the party leadership is vehemently opposed to the candidacy of the eccentric outsider and are not much more excited about Cruz.

Rubio, the great hope of the establishment, might have won one state and finished second in two, but in several other states he was pushed down to third place by either Cruz or Kasich, low enough to leave him with no delegates.

At a rally in Miami, Rubio declared his eagerness for his home state's winner-take-all contest in two weeks, when all 99 delegates will be awarded to the Republican that places first in Florida.

"We are so excited to be home and we are so excited about what lies ahead for America," he said. "We are so excited about what lies ahead for our campaign."

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