Democratic front-runner Hillary Clinton claimed victories in Georgia and Virginia, while rival Bernie Sanders won his home state of Vermont in Super Tuesday elections on the biggest day of the primary campaign.
Donald Trump won the Republican primary in Georgia, while other races were too close to call.
Clinton and Trump were pressing for sweeping victories that could distance them from their party rivals and move them closer to a November presidential election showdown.
Nominating contests were being held Tuesday in 12 of the 50 US states.
Trump, the brash billionaire and reality TV star, has stunned the Republican political establishment by winning three of the first four contests, seizing on the anxieties of voters angry at Washington and worried about terrorism, immigration and an uncertain economy. Using simple terms, and often coarse language, he has soared to the top of polls with his pledge to "make America great again."
Republican officials, fearing a Trump sweep, have been lashing out at his temperament and command of the issues in the hours before voting began.
"You've got a con man and a bully who is moving forward with great speed to grab the party's mantle to be its standard bearer," Norm Coleman, a former senator who backs Marco Rubio, said. "That's almost incomprehensible."
Clinton, once seen as the all-but-inevitable Democratic nominee, has contended with an unexpectedly strong challenge from Sanders, a senator and self-described democratic socialist. But Clinton, like Trump, had also won three of the first four races, and a landslide victory in South Carolina on Saturday bodes well for prospects in important southern states due to her overwhelming support among black voters.
Candidates are vying to win delegates who will vote for them at the parties' conventions in July. For Republicans, 595 delegates were at stake, nearly half of the 1,237 needed for the nomination. Democrats were allocating 865, delegates more than one-third of the 2,383 needed to become the nominee.
Tuesday's vote was critical for the two leading Republicans vying to be Trump's main challenger: Ted Cruz, a firebrand conservative senator from Texas, and Rubio, a Florida senator who has become the favourite of much of the Republican establishment.
Both senators have launched furious verbal attacks on Trump in recent days, but some in the party establishment fear the anti-Trump campaign has come too late.
