The count is still on but Donald Trump has so far won seven states, compared with only two taken by his closest rival, Ted Cruz, and one by Marco Rubio.
Speaking in his home state of Texas, Ted Cruz urged other Republicans to quit the race and join him against Donald Trump.
Democrat Bernie Sanders has won in four states.
Super Tuesday saw 11 states voting, from Massachusetts in the east to Alaska in the north-west. A 12th state, Colorado, held a caucus – won by Bernie Sanders – but does not actually select its delegates until April.
Super Tuesday allocates nearly a quarter of Republican delegates, and about a fifth of Democratic delegates, who will elect their respective presidential candidates at party conventions in July. No candidate has yet won enough delegates to secure their party’s nomination.
Democrat Hillary Clinton, a former secretary of state, and Republican Donald Trump, a property tycoon, entered Super Tuesday as favorites to win the vast majority of states for their respective parties.
In a victory speech, Hillary Clinton appeared to already be looking towards a potential presidential race against Donald Trump, saying: “The stakes in this election have never been higher and the rhetoric we’re hearing on the other side has never been lower.”
Donald Trump insisted that he was a “unifier” who could put internal fighting in the Republican Party behind him.
“Once we get all this finished, I’m going after one person – Hillary Clinton,” he told reporters in Florida, where he has been campaigning ahead of the state’s vote later this month.
Donald Trump insisted he had “expanded the Republican party”, referring to higher turnout from a broad demographic in states that have already voted.
Texas Senator Ted Cruz desperately needed to win in his home state to have any chance of staying in the race.
Pointing to his three primary wins against Donald Trump to date in the season, he told Republicans: “I ask you to prayerfully consider our coming together, united.”
Donald Trump has stunned the Republican establishment to become the party’s front-runner.
He has faced heavy criticism this week over his failure to disavow David Duke, a leader of the white supremacist Ku Klux Klan, who endorsed him.
Donald Trump later said he had on several occasions in the past disavowed David Duke.
Hillary Clinton had already secured three wins in the first four early voting states, polling significantly among blocs of black voters.
Bernie Sanders, who describes himself as a democratic socialist, has put up an unexpectedly strong challenge against her since his sweeping victory in New Hampshire last month.
Addressing cheering supporters at his victory speech in Vermont, Bernie Sanders aimed a jibe at the Republican front-runner saying: “We are not going to let the Donald Trumps of the world divide us.”
The proportion of votes won equates to the number of delegates who will then go on to the Democratic and Republican parties’ national conventions in July to officially choose the nominees for the presidency.
The election itself, on November 8, will see America vote for a successor to Barack Obama.
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