The immigration department is reviewing the visa of a Shia Muslim cleric who toured Orlando in March and argues that homosexual acts are punishable by death under sharia law.

British-born medical doctor and preacher Farrokh Sekaleshfar is giving lectures throughout the Islamic holy month of Ramadan at the Imam Husain Islamic Centre in Sydney's south-west.

Sekaleshfar, who spoke in Orlando in March, told a Michigan audience in 2013 that "death is the sentence for homosexual acts" in Islam and this was "nothing to be embarrassed about".

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