Voting was underway Tuesday in the Midwestern state of Indiana, in what could be the decisive showdown between Donald Trump and Ted Cruz for the Republican Party's nomination in the US presidential elections in November.

"If we win Indiana, it's over," Trump declared at a rally in the state as he hopes to notch a victory to buttress growing expectations that he is the centre-right party's inevitable nominee.

Cruz meanwhile has been painting Indiana as a battleground for the soul of the party and denouncing Trump's style and substance.

"The people of Indiana are the heartland of this country, and we have a choice - we have a choice about our national character; who we will be," Cruz told reporters.

The state would seem to be fertile ground for Cruz, who has received good results in other Midwestern states, and the Texas senator had at one point pulled close to Trump in Indiana polling.

But going into Tuesday Trump led by more than 9 percentage points in an average of opinion surveys by website Real Clear Politics. Some surveys gave him a double-digit lead, with an NBC News/Wall Street Journal poll giving the billionaire businessman an edge of 15 percentage points.

The populist Trump has turned his very wealth into a selling point with many voters.

"He doesn't owe anything to anybody," Duane Hodgin, 72, told dpa outside a polling station in Richmond, Indiana, on Tuesday. "He's rallied a common purpose among the disenfranchised voters turned off by what's going on in Washington."

Jon Hunter, 49, a veteran of the first Gulf War and Trump supporter, said, "The status quo is not working for this country." He believes Trump could improve perception other countries have of the US. "Ten years ago we had a better place in the world" Hunter told dpa. The third remaining Republican presidential candidate, Ohio Governor John Kasich, agreed last month not to invest resources in the state in what was touted at the time as an agreement between Cruz and Kasich to better take on Trump.

Trump had declared himself the "presumptive nominee" after winning primaries last week in five north-eastern states. Despite a strong plurality, he remains well short of the majority - 1,237 delegates - needed to win the nomination at the party's July convention.

Cruz and Kasich are counting on keeping Trump short of that magic number to force a so-called contested convention, in which delegates are free to pick any candidate they chose if no one earns the majority of the delegates outright.

Trump has 956 pledged delegates to Cruz's 546 and Kasich's 153, according to a tally by The New York Times.

If Trump wins Indiana, he could be on pace to achieve a majority of delegates, they said.

Cruz however has vowed to stay in the race even if he falls short in Indiana, where 57 delegates are up for grabs.

"I am in for the distance, as long as we have a viable path to victory, I am competing to the end," he said.

Cruz last week named former Hewlett-Packard boss Carly Fiorina as his vice presidential running mate, in an unusual move designed to widen his support. He also secured the coveted endorsement of Indiana Governor Mike Pence.

On the Democratic side, where 92 delegates are at stake, former secretary of state Hillary Clinton leads rival Bernie Sanders by an average of 6.8 percentage points in polls, according to Real Clear Politics.

Sanders hopes to force a contested convention in the left-leaning party, despite trailing in the delegate count.

Amber Angarita, 30, said she voted for Bernie Sanders. "I think there needs to be a complete shake up of our government system and he's the man to do it," Angarita told dpa.

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