Members of Republican US presidential candidate Donald Trump's family, son Donald Trump Jr. (2nd L), daughter Ivanka (C) and son Eric stand with the New York delegation during the nominating process at the Republican National Convention in Cleveland, Ohio, US, July 19, 2016. [Photo/VCG]

Despite threats of another chaotic day at the Quicken Loans basketball arena in Cleveland, anti-Trump Republican US Senator Mike Lee said efforts by some delegates to block Trump's nomination appeared finished.

"I don't see any way around it," the Utah lawmaker told Reuters.

Trump's campaign has been marked by frequent controversy over his rhetoric on Muslims, Hispanics, illegal immigration and trade, alarming many in the Republican establishment.

Party officials are hoping to use the four-day convention, which began on Monday, to smooth out some of his rough edges and present him as a job creator and a strong hand to combat security threats at home and abroad.

Republicans were also set on Tuesday to place in nomination Indiana Governor Mike Pence, 57, Trump's choice for his vice presidential running mate.