Donald Trump's latest primary wins deal another blow to establishment Republicans

Republican front-runner Donald Trump racked up primary wins in the big prize of Michigan as well as Mississippi and Hawaii on Tuesday, brushing off a week of blistering attacks from the party's establishment and expanding his lead in the White House nominating race.

In the Democratic contest, Bernie Sanders stunned front-runner Hillary Clinton in a narrow Michigan primary upset, giving his upstart campaign new energy. Clinton won in Mississippi, but Sanders' victory is seen as likely to ensure a prolonged fight to pick a candidate for November's general election.

Trump's convincing win in Michigan restored his outsider campaign's momentum and increased the pressure on the party's anti-Trump forces to find a way to stop the brash billionaire's march to the nomination ahead of several key contests next week.

The 69-year-old New Yorker built his victories in Michigan, in the heart of the industrial Midwest, and Mississippi in the Deep South with broad appeal across many demographics. He won evangelical Christians, Republicans, independents, those who wanted an outsider and those who said they were angry about how the federal government is working, according to exit polls.

Trump said in several television interviews on Wednesday he was drawing new voters to the Republican Party and the establishment figures who are resisting his campaign should save their money and focus on beating the Democrats in November.

"If this party came together... nobody could beat it," Trump told NBC's "Today" programme.

The results were a setback for rival John Kasich, governor of Ohio, who had hoped to pull off a surprise win in neighbouring Michigan, and for Marco Rubio, a U.S. senator from Florida who has become the establishment favourite but lagged badly in both Michigan and Mississippi and appeared unlikely to win delegates in either.

Speaking at a news conference in Jupiter, Florida after Tuesday's voting, Trump said Rubio's recent attacks on him had backfired.

"Hostility works for some people; it doesn't work for everyone," the real estate magnate said.

Trump, a former reality TV star, has peppered his campaign with put-downs of rivals and critics. Many mainstream Republicans have been offended by his statements on Muslims, immigrants and women and alarmed by his threats to international trade deals. Trump has dismissed criticism his statements would be harmful to U.S. interests.

Ted Cruz, a 45-year-old U.S. senator from Texas whose recent victories have positioned him as the prime alternative to Trump, won the party's primary in Idaho.

But Trump suggested his rivals had little hope going forward, and took particular aim at Cruz.

'A HARD TIME'

"Ted is going to have a hard time," Trump said of Cruz. "He rarely beats me."

Trump continues to enjoy a wide lead nationally in the Republican race, although Cruz has been climbing over the past week. Among those who identify as Republicans, Trump has settled in at about 40 percent support, according to a five-day rolling average ending on Tuesday in the Reuters/Ipsos poll.

Cruz at 23 percent and Kasich at 11 percent have been on the rise, largely at Rubio's expense.

The Michigan victory sets Trump up for a potentially decisive day of voting next week. On March 15, Ohio, Florida, Illinois, Missouri and North Carolina - like Michigan, states rich in the delegates who will select their party's nominee at July's Republican National Convention - cast ballots.

The Republican contests in Florida and Ohio award all the state's delegates to the winner. If Trump could sweep those two states and pile up delegates elsewhere next week, it could knock home-state favourites Rubio and Kasich out of the race and make it tough for Cruz to catch him.

Anti-Trump Super PACS have spent millions of dollars on advertisements designed to attack Trump's character in Florida.

But Trump's relentless anti-free trade rhetoric and promise to slap taxes on cars and parts shipped in from Mexico resonated in Michigan, which has lost tens of thousands of manufacturing and auto industry jobs.

"The biggest takeaway is that the Republican establishment is in its death throes. The only remaining candidates are 100 percent anti-establishment," said Mark Meckler, an early founder of the conservative Tea Party movement.

"The solid victory in Michigan is based on his populist message about bringing industry back to this country," Meckler said.

Trump said he and Republican U.S. House of Representative Speaker Paul Ryan recently spoke by phone, telling MSNBC "It was a smart call."

In the Democratic race, Sanders told reporters in Florida that the results in Michigan were a repudiation of the opinion polls and pundits who had written off his chances in the state. Opinion polls had shown Clinton with a double-digit lead going into the primary.

The U.S. senator from Vermont, a democratic socialist, said the win showed his political revolution was "strong in every part of the country. Frankly, we believe our strongest areas are yet to come."

Clinton's campaign signalled ahead of Michigan that the race could be tight. Clinton, her husband, former President Bill Clinton, and daughter Chelsea Clinton all campaigned in the state over the past few days trying to garner last-minute votes.