Bernie Sanders has defeated Hillary Clinton in a close vote in Michigan state, breathing new life into his White House bid.

Clinton however breezed to an easy victory in Mississippi, propelled by overwhelming support from black voters, and she now has more than half the delegates she needs to clinch the Democratic nomination.

In winning Mississippi, exit polls showed Clinton winning nine of every 10 black voters.

Al Jazeera's Kimberly Halkett, reporting from Washington, said Sanders had young people to thank for his win in Michigan.

"There's a large percentage of African-American voters there who typically are favouring Mrs Clinton but at the same time, [Sanders'] message of income inequality, of being left behind in a 'rigged economy' resonate with those voters who have felt the impact of globalisation and seen the auto-manufacturing industry really crumble," she said.

"This is a tremendous psychological as well as political victory."

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In his victory speech, Sanders said his "strongest areas are yet to happen", saying he expected to do well on the West coast and in other parts of the country.

"The American people are saying they are tired of a corrupt campaign, finance system and super packs financed by Wall Street and the billionaire class," he said. "They are tired of a rigged economy."

Republican Donald Trump meanwhile swept to victory in both Mississippi and Michigan, expanding his lead in the contest for the Republican nomination.

Trump built his victories in the industrial Midwest and the Deep South with broad appeal across many demographics, winning evangelical Christians, Republicans, independents, those who wanted an outsider and those who said they were angry about how the federal government is working, exit polls showed.

Trump also won the caucuses in Hawaii, while Texas Senator Ted Cruz won the fourth Republican contest held on Tuesday, the Idaho primary.

At a news conference afterwards, Trump said he was drawing new voters to the Republican Party and the establishment figures that are resisting his campaign should save their money and focus on beating the Democrats in November.

"I hope Republicans will embrace it," Trump said of his campaign. "We have something going that is so good, we should grab each other and unify the party."

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Having entered Tuesday's contests facing a barrage of criticism from rival candidates and outside groups, Trump reveled in overcoming the attacks.

"Every single person who has attacked me has gone down," Trump said at one of his Florida resorts.

Trump's Michigan victory sets him up for a potentially decisive day of voting next Tuesday. 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, 69, could sweep those two states and pile up delegates elsewhere next week, it could knock home-state favourites Marco Rubio and John Kasich out of the race and make it tough for Ted Cruz to catch him.