Donald Trump has been formally nominated the US Republican Party's presidential candidate -- two days after he survived an attempt on his life at a rally.

Trump appeared at the Republican National Convention as it kicked off in Milwaukee, Wisconsin, on Monday.

It marked his first public appearance since he was shot and injured during a campaign rally in Pennsylvania on Saturday.

The former president waved and smiled at his supporters with a bandage on his injured right ear.

Trump won a majority of state delegates at the convention. Ohio Senator J.D. Vance was also nominated as his running mate for the November presidential election.

Vance is the author of "Hillbilly Elegy," a bestseller published in 2016. It is a memoir about his upbringing in Ohio, and the life of white working-class Americans in a Rust Belt state where manufacturing has declined.

The 39-year-old senator is known as a staunch supporter of Trump's "America First" policy.

Trump's policy agenda is also deeply reflected in the Republican Party platform approved at the convention.

It calls for stronger measures against immigration, and blanket tariffs on foreign imports.

Trump is due to deliver his acceptance speech on the final day of the convention on Thursday.