The federal government will examine why a controversial Muslim cleric wasn't on a immigration department watch list when he was granted a visa to come to Australia.
British-born Farrokh Sekaleshfar voluntarily boarded a flight at Sydney Airport on Tuesday night ahead of the immigration department's decision to revoke his visa.
His visit sparked outrage, in the wake of the Orlando gay nightclub massacre in the US, after it emerged he had previously preached the death sentence for homosexual acts.
Prime Minister Malcolm Turnbull said it was difficult to track people when most UK tourists are allowed to come to Australia through an electronic visa processing service.
"The moment this man's presence was drawn to our attention ... the minister acted decisively and his visa was revoked at 7 o'clock last night," Mr Turnbull told Alan Jones on 2GB radio on Wednesday.
Immigration Minister Peter Dutton has defended his department's handling of the case.
"It's difficult for the department to go through the Facebook or social media postings of millions of millions of people each year who seek visas," he said.
When information came to hand the department acted quickly.
Federal Attorney-General George Brandis said Australia's electronic visa system processed millions of applications each year.
"Not everyone who has odious or hateful views is necessarily going to be picked up by that system," he told reporters south of Brisbane.
"What is important here is when this man was shown to have expressed these odious, hateful and homophobic views, my colleague Mr Dutton acted very swiftly and he was out of the country in a matter of hours."