Donald Trump has vowed to beat Hillary Clinton in November's US election as the two cement their spots as frontrunners for their parties in the race for the White House.

The Republican and Democratic hopefuls have dominated so-called Super Tuesday - both winning in seven of the 12 states picking nominees.

Trump's conservative rival Texas Senator Ted Cruz breathed a sigh of relief after a crucial win in his home state, and in Oklahoma.

During speeches overnight - both Trump and Clinton - have turned their sights on each other.

With the Republican candidate promising to "go after" the former First Lady.