Hillary Clinton and Donald Trump launched their two-week scramble to the finish line of the US presidential race on Monday, with the billionaire Republican dismissing the polls to insist he's "winning" the race.

"This is bigger than Brexit, what's going on," the 70-year-old Trump told a rowdy rally in Florida, referring to Britain's shock June vote to leave the European Union.

The Democrat Clinton, 68, sought to cement her lead over her White House foe by conquering swing states including Florida, North Carolina and Ohio where early voting has already begun, as the rivals blitz crucial battlegrounds where the race will be won or lost on Nov 8.