Donald Trump has officially clinched the Republican nomination for US president as speakers hammered Democrat Hillary Clinton on day two of the Republican National Convention.

Trump is expected to accept the nomination on Thursday after state delegates formally selected him.

The theme of Tuesday in Cleveland was "Make America Work Again".

However, the speakers focused almost exclusively on attacking Clinton, the likely Democratic nominee.

New Jersey Governor Chris Christie, a former prosecutor, held a mock trial for Clinton as the crowd chanted "lock her up".

Trump's children spoke, including his youngest daughter Tiffany Trump, whose mother is former model and dancer Marla Maples.

She told some personal stories about her father scribbling notes in her school report cards and how excited she becomes when introducing him to her friends.

Her father is a "natural-born encourager" who has motivated her to work hard, she said.

His son Donald Trump Jr described him as his best friend and role model.

"When people tell him it can't be done, that guarantees it will get done," he said of his father.

He said Clinton was a risk the US cannot afford to take and that "if she were elected, she would be the first president who can't pass a background check".

Trump addressed the audience via a live-stream and said the nomination was an honour.

"This is a movement, but we have to go all the way," he said. "This is going to be a leadership that puts American people first."