The British-born Sheik Farrokh Sekaleshfar is Australia on a speaking tour and says he will abide by any action the Australian government takes.
It was these comments made in the United States three years ago that have brought the cleric under constant scrutiny.
"Death is the sentence, I mean look, it's nothing to be embarassed about this, death is the sentence, we have to have that compassion for people. With homosexuals it's the same. Out of compassion let's get rid of them now."
The Immigration Department only became aware of Sheik Farrokh Sekaleshfar a few days ago and is now reviewing whether his visa should be revoked.
In an interview with the A-B-C, the cleric denies having advocated the death penalty for homosexuals, in countries that don't abide by Islamic law.
"Maybe shouldn't have been published on video, on Youtube. This time they're connecting the massacre. They're connecting me to that - forgive me for saying - that animal."
Prime Minister Malcolm Turnbull says there's a zero tolerance for hate-preachers in Australia.
"As you know, this is a legal matter, and has to be dealt with in the appropriate way. But his visa is being reviewed at the direction of the minister, even as we speak."
Connections are being drawn between Farrokh Sekaleshfar's comments and the mass shooting at the gay nightclub in Orlando.
But in an interview with the A-B-C, Mr Sekaleshfar denies having any connection to the gunman Omar Mateen and says his comments of three years ago would not have influenced the attacker.
Sean Mulcahy from the Victorian Gay and Lesbian Rights Lobby says the Sheik's comments are worrying.
"While the Sheik is engaging in theological debate around homosexuality, what people are hearing is a message of hate. These words can be incredibly damaging, particularly to young as well as vulnerable lesbian, gay, bisexual, transgender and intersex people. I don't think it's the Sheik's intention to initiate violence, he's not out there calling for the killing of LGBTI people. But my concern is that others could interpret this and could interpret his words to a call to arms."
Australian-born Peter Tatchell is a gay activist in the United Kingdom.
Mr Tatchell says those who advocate death to other human-beings should not be allowed in Australia.
He says the Sheik must be investigated to determine what his actual beliefs are.
"Presumably this stems from his understanding of Sharia law and of course we also know that Sharia law prescribes the death penalty for Muslims who turn away from the faith, blasphemers and women who have sex outside of marriage. So this man is preaching some pretty ghastly ideas and I think he needs for investigation to determine exactly what he does believe and what he's advocating because I suspect it must be probably must be much, much wider than merely advocating death to gay people."
The sheik says he will accept whatever decision is made by the government over his visa.
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