A Ugandan-born politician is leading the race to become the mayor of New York City in the United States.

Zohran Mamdani, 33, has stunned the US political establishment after pulling ahead in New York City's mayoral Democratic primary.

If the son of renowned Ugandan academic Mahmood Mamdani and celebrated filmmaker Mira Nair wins the race, he will replace Eric Adams and become New York City's first Muslim mayor.

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With 91 per cent of ballots counted by Tuesday night, Mamdani led with 43.5 per cent of the vote, ahead of former New York Governor Andrew Cuomo who trailed at 36.4 per cent.

Born in Kampala in 1991, Zohran Kwame Mamdani moved to the United States at the age of seven. He had left Uganda two years earlier for South Africa when his parents relocated for academic and creative work.

If confirmed as the Democratic nominee, Mamdani will be assured of becoming the city's 11th mayor in November. His other opponent in the general election, incumbent mayor Eric Adams, is running as an independent.

The socialist politician's candidacy, endorsed by Democrats Alexandria Ocasio-Cortez and Bernie Sanders, has been hailed as a rebuke to the centrist Democratic establishment.