US Senator Ted Cruz was loudly booed by the Republican National Convention on Wednesday as he declined to endorse the party's nominee and his former rival Donald Trump.

Cruz congratulated Trump on his nomination after beating 16 other candidates in the party primaries. He initially was received warmly, but the boos came when it became clear he wasn't going to endorse Trump as he had pledged to do.

Instead, Cruz delivered a speech outlining the conservative principles he believes undergird the party that only once mentioned Trump by name.

He urged voters not to stay home on election day in November but did not say for whom they should vote.

"Stand, and speak, and vote your conscience, vote for candidates up and down the ticket who you trust to defend our freedom and to be faithful to the Constitution."

By Wednesday most of the delegates appeared to had come to terms with Trump's candidacy. A minority of delegates had earlier sought to disrupt the proceedings in favour of an alternate candidate.

Several top party officials skipped the convention, highlighting divisions, but some delegates were optimistic the party will ultimately come together.

"I hope we get to a point where we're all one team. We are not there yet," said Isaac Schultz, a 25-year-old delegate from Minnesota, who said Trump would deliver a message of unity when he speaks on Thursday.

There have been vocal calls for party unity, including from radio host Laura Ingraham, who forcefully called on Cruz to "honour your pledge to support Donald Trump. Do it now tonight."

When he was done speaking, Cruz stood accused of using the spotlight to position himself to run for president again in 2020.

Former speaker of the House Newt Gingrich sought to spin Cruz's remarks in a positive light, saying Trump was the only candidate who met the senator's criteria of protecting the Constitution.

Relations also remained frosty between the Trump camp and former rival Ohio Governor John Kasich, the last competitor to exit the race. Kasich took the exceptional step of staying away altogether from the convention hosted by his state.

The New York Times reported that Trump had repeatedly sought to get Kasich to serve as his vice president, offering him widespread control over government policy, but that the governor had turned him down. The Trump campaign disputed the account provided by an unnamed Kasich advisor.

"I think Kasich is hurting himself," Nevada delegate and Trump supporter George Assad told dpa. "I think he owes it to the party to put it aside and seek a cause greater than his own self interest."

Another former rival, Senator Marco Rubio of Florida, who has issued only a tepid endorsement of Trump, is not at the convention but appeared in a recorded video message.

The evening culminated in a speech by Indiana Governor Mike Pence to accept the party's vice presidential nomination.

Pence extensively praised Trump and bashed Clinton as a political insider out for her own advancement.

"It's change versus status quo, and my fellow Americans when Donald Trump becomes president of the United States of America the change will be huge."

He warned that the Clinton machine would go full force against Trump but said it wouldn't be enough to defeat a candidate like Trump who has captured the spirit of the country.

"We will win the hearts and minds of the American people with an agenda for a prosperous and stronger America," he said.

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