Clinton won in Texas, Massachusetts, Arkansas, Alabama, Tennessee, Georgia and Virginia. The wins reflected her strength in the South, where black voters are an important part of the Democratic base.
In the Democratic race, Clinton has faced a tougher-than-expected challenge from Bernie Sanders, a Vermont senator and self-described democratic socialist who has energized supporters with his calls for a political revolution.
Clinton was assured of winning at least 467 of the 865 delegates at stake on Super Tuesday, while Sanders picked up at least 286 delegates. Overall, Clinton now has at least 969 delegates.
With results still coming in, Trump had won at least 192 delegates Tuesday, while Cruz picked up at least 132. Overall, Trump leads the field with 274 delegates, with 1,237 needed for the nomination.
In six of the states voting Tuesday, large majorities of Republican voters said they supported a proposal to temporarily ban all non-citizen Muslims from entering the United States, an idea championed by Trump.
Tuesday's results did little to clarify which of two senators - Ted Cruz or Marco Rubio - might emerge as Trump's main Republican rival, with both vowing to fight on despite weak performances
Trump's dominance has rattled Republican leaders, who fear the billionaire real estate mogul and former reality TV star is unelectable against Clinton in November.
Clinton won seven of 11 states and Trump did at least as well, as the front-runners padded their leads in the all-important delegate counts that determine the parties' nominees.
Clinton turned away from rival Bernie Sanders and set her sights on Trump as she addressed supporters during a victory rally in Miami.
Clinton won in Texas, Massachusetts, Arkansas, Alabama, Tennessee, Georgia and Virginia. The wins reflected her strength in the South, where black voters are an important part of the Democratic base.