Thirteen months after launching an improbable bid for the White House, Donald Trump captured the 2016 Republican presidential nomination on Tuesday, having vanquished 16 party rivals, warred with much of its establishment and provoked controversy at every turn.

His eldest child, Donald Trump Jr, announced the support of New York, their home state, during a roll-call vote at the Republican National Convention, ensuring Trump had the majority of delegates - 1,237- needed to contest the Nov 8 US presidential election against presumptive Democratic nominee Hillary Clinton.

With three of the candidate's other children at his side, the younger Trump said: "It is my honor to be able to throw Donald Trump over the top in the delegate count tonight."

"Congratulations, Dad. We love you," he said.

Trump's Democratic rival, Clinton, was quick to respond, tweeting after the vote: "Donald Trump just became the Republican nominee. Chip in now to make sure he never steps foot in the Oval Office."

Trump won with 1,725 delegates, followed by US Senator Ted Cruz of Texas with 475 delegates, Ohio Governor John Kasich with 120 and US Senator Marco Rubio of Florida with 114. Three other candidates emerged with a total of 12 delegates.

After the presidential vote, the convention by voice vote nominated Indiana Governor Mike Pence, 57, Trump's choice for his vice-presidential running mate.

Speaking to the convention for the first time since winning the nomination, Trump appeared on a video screen from New York promising to win the election in November, create jobs, strengthen the military, safeguard US borders and "restore law and order" in the United States.

The state-by-state vote to put Trump's name in nomination took place a day after opponents staged a failed attempt to force a vote opposing his candidacy, and after a speech by his wife, Melania, drew accusations of plagiarism.

A wealthy New York real estate developer best known to Americans for his starring role in a long-running TV show, The Apprentice, where his catchphrase was "You're fired," the 70-year-old Trump was a long shot when he entered the race for the Republican nomination more than a year ago, having never held elected office.

Speaker after speaker on Tuesday, the second day of the four-day convention at Cleveland's Quicken Loans basketball arena, took aim at Clinton, presenting her as out of touch with the concerns of ordinary Americans and the inheritor of President Barack Obama's "oppressive" administration.