UPDATED 6.36PM: Republican front-runner Donald Trump has swept to a commanding victory in Indiana, putting him on a glide path to the party's presidential nomination as Ted Cruz finally ended his campaign.

The New York billionaire won decisively in a state where Cruz, his nearest rival, had hoped to show he was still a factor in the race for the Republican nomination.

Republican National Committee chairman Reince Priebus called Trump the party's presumptive nominee in a tweet and said, "We all need to unite and focus" on defeating Clinton.

As the vote returns flowed in, Cruz announced that he has ended his campaign at an event in Indianapolis, with his wife, Heidi, at his side. Cruz, 45, sounding beaten but defiant, said he no longer sees a viable path to the nomination.

"Together we left it all on the field in Indiana," said Cruz, a US senator from Texas.

"We gave it everything we got. But the voters chose another path, and so with a heavy heart, but with boundless optimism for the long-term future of our nation, we are suspending our campaign."

Auckland University politics and international relations lecturer Maria Armoudian told Rachel Smalley Cruz's key failure was his lack of ability to relate to the masses.

"He was definitely popular among a small group of very religious and very right-wing republicans."

She said Trump's simple solutions to complex problems have given him a wide following but only of those with no real understanding of politics.

"This is what Donald Trump does, he creates an enemy, he insults an enemy, he professes to be the fixer of all."

Trump was on track to take over 50 per cent of the vote. Ohio Governor John Kasich was running a distant third.

Trump told supporters his heart goes out to Cruz and his family.

"He is one hell of a competitor. He is a tough, smart guy and he has got an amazing future. He's got an amazing future."

In his victory speech Trump told supporters America's forgotten how to win.

"We've been losing all the time. We lose with our military, we can't beat ISIS. We lose with trade, we lose with borders. We lose with everything. We're not going to lose. We're going to start winning again."

Trump told those gathered he thinks he'll be up against Clinton, and she's not the woman for the White House.

"She will not be a great president. She will not be a good president. She will be a poor president. She doesn't understand trade."

On the Democratic side, Bernie Sanders won the presidential primary with 53 per cent of the vote compared with 47 per cent for Hillary Clinton, with 64 per cent of precincts counted.

But it's a win that won't change the reality of the Democratic race.

Sanders told CNN he started his entire campaign behind Hilary Clinton.

"We've been fighting uphill from day one, we will continue to fight uphill and I think we still have a narrow path toward victory."

The Vermont senator is far behind the former secretary of state in the delegate count. Clinton entered the night with 91 per cent of the delegates she needs to become the first woman nominated by a major party.

Sanders told CNN that corporate greed is destroying America's middle class.

"I don't think the American people want to see that any more. They want some moral responsibly on the part of corporate America, to respect their employees, to respect their consumers of this country."

Cruz had been counting on a win in Tuesday's primary to slow the New York businessman's progress towards the nomination. But Trump rode momentum from wins in five northeastern states a week ago to wrest Indiana from Cruz, whose brand of Christian conservatism had been expected to have wide appeal in the state.

David Yepsen, director of the Paul Simon Public Policy Institute at Southern Illinois University, said the Republican race is over.

"Cruz is certainly young enough to fight again another day. Kasich's a serious guy but if [he] stays in this he could look silly," Yepsen said.

The loss for Cruz was a sour ending to a rough day in which he got entangled in a harsh back-and-forth with Trump.

It began when the billionaire repeated a claim published by tabloid newspaper the National Enquirer that linked Cruz's father, Cuban emigre Rafael Cruz, with President John F. Kennedy's assassin Lee Harvey Oswald.

Campaigning in Evansville, in the state's southwest corner, Cruz sounded deeply frustrated by the bombastic real estate mogul, who has ripped Cruz at every turn.

"The man cannot tell the truth but he combines it with being a narcissist," Cruz said, "a narcissist at a level I don't think this country has ever seen."

Cruz termed Trump a "serial philanderer" - likely as part of his strategy to try to win the support of evangelical voters.

Trump, in response, said Cruz had become "more and more unhinged".

The only hope Kasich has for becoming the Republican nominee is to somehow deny Trump the 1237 delegates he needs to win the nomination outright and force Republicans at their July convention in Cleveland to choose one of them.

Kasich vowed to stay in the race.

"Tonight's results are not going to alter Governor Kasich's campaign plans," Kasich senior strategist John Weaver said in a campaign memo. "Our strategy has been and continues to be one that involves winning the nomination at an open convention."