Democratic US presidential candidate Hillary Clinton speaks to supporters at a primary night party in Miami, March 1, 2016.[Photo/Agencies]

Republican Donald Trump and Democrat Hillary Clinton took big steps toward securing their parties' presidential nominations on Tuesday with a series of state-by-state victories, but their rivals vowed to keep on fighting.

On Super Tuesday, the 2016 campaign's biggest day of nominating contests, Trump, 69, and Clinton, 68, proved themselves the undisputed front-runners.

Now they are under pressure to show they can unify voters in their respective parties and avoid a potentially disastrous split in their ranks that could hurt them in the Nov. 8 election.

US networks projected Trump won seven states with victories stretching into the deep South and as far north as Massachusetts, adding to a sense of momentum he had built last month by winning three of the first four contests.

Clinton's victories in seven states were just as impressive but in many ways predictable, propelled by African-American voters in southern states like Arkansas, where she and former President Bill Clinton began their political careers.

Trump's rivals Ted Cruz, a US senator from Texas, and Marco Rubio, a US senator from Florida, emphasized their determination to remain in the race.

Cruz, 45, won his home state of Texas and neighboring Oklahoma, bolstering his argument he had the best chance to stop the brash billionaire. Rubio, favorite of the Republican establishment, was projected the winner in Minnesota, his first victory.

Clinton's rival Bernie Sanders, a democratic socialist US senator from Vermont, also won his home state along with Colorado, Minnesota and Oklahoma and vowed to pursue the battle for the nomination in the 35 states yet to vote. He lost to Clinton in Massachusetts, a fifth state he had hoped to win.

Super Tuesday was the biggest single day of state-by-state contests to select party nominees for the Nov. 8 election to succeed Democratic President Barack Obama.