Ted Cruz has suspended his White House campaign after suffering a crushing defeat in Indiana's primary, leaving the road wide open for Donald Trump to seize the Republican nomination.

Key points: Ted Cruz suspends campaign after Trump wins Indiana primary

Ted Cruz suspends campaign after Trump wins Indiana primary Republican chief says Trump is now 'presumptive nominee'

Republican chief says Trump is now 'presumptive nominee' Bernie Sanders defeats Hillary Clinton in Democratic primary

"From the beginning, I've said that I would continue on as long as there was a viable path to victory," the Texas senator told supporters in Indianapolis.

"Tonight, I'm sorry to say, it appears that path has been foreclosed.

"We gave it everything we've got, but the voters chose another path," said Senator Cruz, whose withdrawal leaves the low-polling John Kasich as Mr Trump's sole challenger.

The New York billionaire was quickly projected to be the winner by television networks shortly after polling places closed in the Midwestern state.

Mr Trump was on track to take well over 50 per cent of the vote, eclipsing Senator Cruz, while Ohio Governor Mr Kasich was running a distant third.

Speaking after at a victory, Mr Trump accompanied by his wife Melania and other family members, called Indiana a "tremendous victory" and immediately directed fire at Democratic frontrunner Hillary Clinton.

"We're going after Hillary Clinton," he said, speaking at Trump Towers in New York.

"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, Senator Bernie Sanders mounted a come-from-behind victory in Indiana's Democratic primary, denying Mrs Clinton a feather in her cap as she eyed their party's presidential nomination.

Senator Sanders, a self-declared Democratic socialist, was ahead of Mrs Clinton by 53.2 per cent to 46.8 per cent with about three-quarters of precincts reporting, although Mrs Clinton remained well ahead in the delegate battle for the nomination.

After Senator Cruz dropped out of the race, Republican Party chief Reince Priebus declared on Twitter that Mr Trump would be the presumptive Republican presidential nominee.

"Donald Trump will be presumptive @GOP nominee, we all need to unite and focus on defeating @HillaryClinton," Mr Priebus said, virtually assuring the billionaire real estate mogul will represent the Republicans in the November election.

Mr Trump is likely to formally wrap up the nomination on June 7 when California votes.

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

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

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Campaigning in Evansville, Indiana, Senator Cruz sounded deeply frustrated by the bombastic real estate mogul, who has ripped the conservative Senator Cruz at every turn.

"This is just kooky. The man is utterly a moron," Senator Cruz said.

"A caricature of a braggadocious, arrogant buffoon who builds giant casinos with giant pictures of him everywhere he looks.

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

Senator Cruz also termed Mr Trump a "serial philanderer".

In response, Mr Trump said Senator Cruz had become "more and more unhinged".

Reuters