Donald Trump is poised to become the Republican Party's presidential nominee, with rival candidate Ted Cruz quitting the race today after being crushed by the frontrunner in the Indiana primary.

"We had a tremendous victory tonight," the billionaire said from his Trump Tower headquarters in New York City.

Republican National Committee chairperson Reince Preibus tweeted that Trump is now the conservative party's "presumptive" nominee and encouraged party supporters to focus on the November general election.

"We all need to unite and focus on defeating @HillaryClinton #NeverClinton," Preibus wrote.

The party has been deeply divided by Trump's candidacy, with some leading Republicans waging a #NeverTrump Twitter campaign against the political neophyte.

The Cuban-American Cruz, who had sought to be the first major-party Latino presidential nominee, reminded supporters that he had vowed to keep fighting as long as he saw a path to victory.

"Tonight I'm sorry to say that path has been foreclosed," the Texas senator said.

"We left it all on the field in Indiana. We gave it everything we've 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."

US broadcasters declared Trump the winner in Indiana based on early returns and exit surveys as soon as the last polls closed. He had 53 percent of the vote to 37 percent for Cruz.

Cruz had tried to make Indiana a bulwark against Trump winning the 1,237 delegates needed to secure the nomination at the Republican convention in July.

With Trump winning all or nearly all of Indiana's 57 delegates, he now has 1,007 pledged delegates, according to a New York Times tally.

Minutes after calling his rival "lyin' Ted Cruz" on Twitter, Trump had kinder words when he quit, calling Cruz "one hell of a competitor".

The populist Trump has turned his vast 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.

"He's rallied a common purpose among the disenfranchised voters turned off by what's going on in Washington."

Trump still remains shy of the delegates needed, but there is little doubt he will easily secure them in the remaining contests.

Ohio Governor John Kasich remains the only other Republican candidate in the race and said on Tuesday he would continue until Trump gets all the delegates needed for the nomination.

On the Democratic side, former secretary of state Hillary Clinton remains the clear front-runner, but Vermont Senator Bernie Sanders is continuing to wage his surprising upstart campaign after winning Indiana with 53 percent of the vote to 47 percent for Clinton.

Sanders hopes to force a contested convention in the left-leaning party, despite trailing in the delegate count. He now has 1,409 pledged delegates to Clinton's 1,699, but she has many more of the so-called super delegates, who are party officials free to vote for whomever they chose.

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

In a preview of the months of campaigning yet to come, Trump turned his attention to the general election.

"We're going after Hillary Clinton. She will not be a great president, she will not be a good president - she will be a poor president," he said.

Clinton's campaign meanwhile sought to use the spectre of a Trump presidency to spur donations from her supporters, while her campaign called chairman called the presumptive Republican nominee unfit to be president.

"Throughout this campaign, Donald Trump has demonstrated that he's too divisive and lacks the temperament to lead our nation and the free world," John Podesta said.

"With so much at stake, Donald Trump is simply too big of a risk."

- dpa