Addressing jubilant supporters at Trump Tower in New York after romping to his seventh straight state-wide victory, the real estate mogul promised them: "We're going to win in November, and we're going to win big, and it's going to be America first."
Trump won at least 51 of 57 possible delegates awarded in Indiana, according to the Associated Press news agency delegate tracker. His victory in the state pushed him to 1,047 delegates of the 1,237 needed to clinch the nomination, compared with 153 for Kasich.
Cruz had 565 delegates before suspending his campaign.
"This phenomenon is just amazing," Peter Mathews, a political analyst, told Al Jazeera. "Trump seems to have got free television time. He got an estimated $1bn of free time during the election."
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Trump's immediate challenge is to unite deep fissures within the Republican Party as many party loyalists are appalled at his bullying style, his treatment of women and his signature proposals to build a wall on the border with Mexico and deport 11 million illegal immigrants.
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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.
The former reality TV star himself called for unity in a speech at a victory rally that was free of his usual bombast and flamboyance.
Calling Indiana a "tremendous victory", he immediately directed fire at Democratic frontrunner Hillary Clinton.
"We're going after Hillary Clinton," he said. "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."

Clinton upset

Clinton on Tuesday suffered an upset in Indiana as her rival Bernie Sanders mounted a come-from-behind victory, denying the former secretary of state a feather in her cap as she seeks their party's presidential nomination.

Sanders, a self-declared socialist, beat Clinton by 53.2 percent to 46.8 percent with about three quarters of precincts reporting - although Clinton remained well ahead in the overall delegate battle for the nomination.
"Bernie Sanders was behind several points just a few weeks ago. Thousands were turning to his rallies even in thunderstorms to hear what he had to say," Al Jazeera's Alan Fisher, reporting from Indianapolis, said.
"A narrow victory in Indiana is enough to re-inject his campaign with momentum and for him to say that he is going to take it all the way to Democratic convention in Philadelphia in the summer."
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As the race was called overwhelmingly in Trump's favour, Cruz conceded to supporters in Indianapolis that he no longer had a viable path forwards.
"We left it all on the field in Indiana," Cruz said. "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."
Al Jazeera's Fisher said that Indiana had become a pivotal point in the race.
"On the Republican side, Cruz lost the primary by a significant margin. His appeal to voters simply did not work," he said.
Trump, who has never held public office, is likely to formally wrap up the nomination on June 7 when California votes, although Ohio Governor John Kasich vowed to stay in the race as his last challenger.
Cruz conceded to supporters in Indianapolis that he no longer had a viable path forwards [AP]
Source: Al Jazeera and agencies