Republican front-runner Donald Trump on Tuesday won two more states
Senator Ted Cruz, Trump's closest competitor, won the primary in the Western state of Idaho. Results from the Republican caucus in the Pacific island state of Hawaii were expected later.
Meanwhile, Democratic front-runner Hillary Clinton rolled to victory in Mississippi on the Gulf Coast but in the Midwest unexpectedly lost to Senator Bernie Sanders in Michigan, leaving the race for the left-leaning party's nomination unresolved.
After Tuesday's victories, the billionaire Trump predicted that his campaign for the nomination would soon be unstoppable.
"There's only one person that did well tonight: Donald Trump," he said in an appearance at a golf course he owns in Florida, where Republicans hold a pivotal primary vote on March 15.
Trump said he expects to "do really well in Florida" and in Ohio, another populous state that votes the same day. The two large states are the first to assign their delegates to the party's July nominating contest by winner-take-all rules.
Illinois, Missouri and North Carolina also vote March 15. Before then, Republicans hold votes Saturday in Wyoming and Washington, DC.
The real estate magnate ridiculed his three remaining Republican rivals: "They're pretty much all gone. ... We started with a field of 17 [Republican candidates], and now we're down to four, and I want to close things out."
In Michigan, Trump had more than 36 per cent, compared to Cruz with 25 per cent and Governor John Kasich of neighbouring Ohio with more than 24 per cent.
Clinton, speaking at a rally in Cleveland, Ohio, drew a distinction between her Democrats and their conservative rivals.
"We are better than what we are being offered by the Republicans," Clinton said.
"Running for president shouldn't be about delivering insults. It should be about delivering results," she said.
Sanders thanked voters for an "enormously successful night" in Michigan, where he led with 50 per cent of the vote, compared to Clinton's 48 per cent, with 97 per cent of the vote counted.
Sanders said voters "repudiated the pundits" who had predicted a Michigan win for Clinton and that the results demonstrated that his "people's revolution ... is strong in every part of the country."
The contests follow weekend primaries and caucuses that saw wins for Cruz in Kansas and Maine, Florida Senator Marco Rubio in the Caribbean territory of Puerto Rico, and Trump in Louisiana and Kentucky.
Trump's opponents, including several deep-pocketed conservative groups, are pouring money into television ads attacking the political neophyte, whom they fear could harm the Republican Party with his divisive rhetoric.
Cruz hopes to ride his strong showing Saturday to become the top pick among anti-Trump voters, as Rubio has faltered despite support from key party officials.
Florida, as Rubio's home state, and Kasich's Ohio are considered must-wins for each of the two candidates, who have fallen well behind Cruz as Trump's closest rival.
Clinton, who has won easily across the South, received 83 per cent of the vote in Mississippi.