Donald Trump declared himself a champion of the American people as he claimed the Republican Party's presidential nomination at the party convention in Cleveland, Ohio late Thursday and looked forward to a November contest against Democrat Hillary Clinton.

"I’m with you – the American people,” he said, "I am your voice."

Trump vowed to put the United States first by restoring law and order in the wake of a series of high profile police shootings, by restricting illegal immigration, by rejecting globalism and renegotiating trade deals and by restore the US economy.

"Together, we will lead our party back to the White House, and we will lead our country back to safety, prosperity and peace," he said.

But while Trump vowed to defeat Islamic terrorists, he took a more isolationist stance than the party has taken in recent decades, calling NATO obsolete and urging a renegotiation of trade deals.

"Americanism, not globalism, will be our credo," Trump said.

He sought to contrast himself with Clinton whom he claimed was only out for herself and had advocated dangerous policies as secretary of state. The former US secretary of state will be formally nominated next week at the Democrats' party convention in Philadelphia.

The thousands of delegates and guests delivered huge cheers for Trump and boos for Clinton, including chants of "lock her up."

As long as the United States is led by politicians who will not put America first, "then we can be assured that other nations will not treat America with respect," Trump said.

But the shift away from traditional Republican policies on trade left at least some uneasy, including delegate Arto Leino, 77, a New Hampshire delegate who had originally supported Jeb Bush.

He said he was left wondering, "How in the world he's going to do all this?" Still, he vowed he would vote for Trump in November. "We have to have unity, in the party otherwise it's no party."

Trump was introduced by his daughter, Ivanka Trump, who said he was an outsider with big ideas for change in the United States.

"Real change, the kind we have not seen in decades, is only going to come from outside the system, and it's only going to come from a man who has spent his entire life doing what others said cannot be done," she said.

Trump said as president he would speak for ordinary Americans, including those ignored by politicians.

"Every day I wake up determined to deliver for the people I have met all across this nation that have been neglected, ignored and abandoned," he said.

He said he would work for those who have lost jobs due to trade deals and other "forgotten men and women of our country - people who work hard but no longer have a voice. I am your voice," he said.

The delegates on Tuesday formally nominated Trump as the party's standardbearer at a convention that has highlighted party divisions almost to the same degree that party rank and file has gushed about Trump's potential.

"He will change the world," said William Wilson of Florida, pointing to Trump's pledge to keep America safe and "finish off" terrorists.

When Trump announced his candidacy more than a year ago, he was thought unlikely to win in a crowded field of 17 candidates full of experienced politicians and rising Republican stars. But he quickly gained a popular following and knocked off his opponents one by one.

Trump nodded to the unlikelihood of his candidacy by telling the crowd: "Remember, all of the people telling you that you can’t have the country you want are the same people telling you that I wouldn’t be standing here tonight."

Former rival Senator Ted Cruz was booed by thousands of convention delegates on Wednesday night when he took the stage and pointedly failed to endorse Trump. Several top party officials also skipped the convention, highlighting divisions.

The Trump campaign however stressed that the party would unite as it prepares to shift course after a fractious primary season.

Georgia delegate John Westmoreland told dpa he hoped Trump would bring the party together.

"I just hope he can speak about unity and get the party together," he said.

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