Ohio Governor John Kasich will drop out of the Republican presidential race after Donald Trump's victory in the Indiana primary virtually assured he will be the party's nominee, US media report citing senior campaign officials.

Trump's last remaining Republican opponent cancelled a planned press conference outside Washington on Wednesday morning and said he would instead make a statement in Ohio at 5 pm (2100 GMT) fuelling speculation that he was ending his presidential run.

Kasich had only won his home state of Ohio, but had vowed Tuesday night to remain in the race until Trump actually reached the 1,237 delegates needed at the party convention to win the nomination.

Trump's nearest opponent, Ted Cruz, dropped out Tuesday evening after losing badly in Indiana, where he had invested substantial resources in what his campaign portrayed as a last stand against Trump.

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

Republican National Committee chairman Reince Preibus tweeted that the result meant 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.

Trump drew 53 per cent of the vote to 37 per cent for Cruz in Indiana, which Cruz had tried to make 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.

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

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 per cent of the vote to 47 per cent 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.

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."

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