Republican US presidential candidate Donald Trump has introduced Mike Pence as his running mate, calling the Indiana governor his "first choice".

At a formal announcement in New York on Saturday, Trump also acknowledged that one of the reasons he selected Pence was to promote unity within the Republican Party.

Pence headed back to Indiana later in the day, where he urged supporters to vote for Trump whom he called a good man who will make a "great president".

Pence, 57, has served as governor of Indiana since 2013 and also represented the state in Congress for more than a decade.

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Trump has signalled that he wanted an experienced politician to help his presidential ticket because he is a political outsider with no experience in governing.

Trump met Pence on Wednesday in Indiana, as he had done with other candidates he has said are his top choices.

Trump himself had said that Pence was among his top picks, along with New Jersey Governor Chris Christie and former Speaker of the House Newt Gingrich.

Trump is to be formally nominated as the party's candidate for the November 8 election at the Republican National Convention in Cleveland. Traditionally, the vice presidential choice is used to build enthusiasm among party loyalists.

Pence is seen as a fiscal and social conservative who can appeal to a broad swath of voters in the centre-right party so that Trump can make himself more palatable to Republicans who have been wary of his candidacy.

Pence points to his work enacting the largest tax cut in state history and lowering business taxes, balancing the state's budget and efforts to draw businesses to the state.

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As governor, Pence came under fire after signing a so-called religious freedom bill that opponents said would have allowed businesses to discriminate against gays, but he later revised the legislation.

Pence, however, has disagreed prominently with Trump on a number of issues; he has spoken out against the Republican presidential candidate's controversial call for a ban on Muslims entering the US and on trade deals.

Pence had been in a tight re-election bid for governor and faced a Friday deadline to withdraw from that race in order to run for vice president instead.