A British-born Shia Muslim cleric who toured Orlando this year and previously preached that "death is the sentence" for homosexual acts has left Australia, after the government launched an urgent review of his visa.

Farrokh Sekaleshfar had been giving a series of lectures at an Islamic center in Sydney on the topic of spirituality throughout Ramadan.

Sekaleshfar said in a lecture in Michigan in 2013 that in an Islamic society, the death penalty should be carried out for gay people who engaged in sodomy.

"Out of compassion, let's get rid of him now, because he's contaminating society," Sekaleshfar said in a talk at that time, according to a recording available online.

There is no evidence of any link between his comments and the American Muslim man who killed 49 people in a gay nightclub in Orlando on Sunday, the deadliest mass shooting in the United States.

Sekaleshfar told Reuters on Monday he condemned the Orlando shooting as a "barbaric act of terror that was in no way justified" and expressed "utmost, sincere condolences" to the friends and families of the victims.

Sekaleshfar told the Australian Broadcasting Corp that his decision to leave was voluntary and that he had not been asked to go by the government. The network showed footage of him entering Sydney airport, and said he was flying to Dubai.

"It's a decision which IHIC thought it was in my best interests and for the best interests of the community. And I didn't want to go against the committee's decision," he said, referring to the Imam Husain Islamic Center, where he had been giving talks on religion.

Australian Prime Minister Malcolm Turnbull told reporters on Tuesday he has "zero tolerance for people to come to Australia who preach hatred" and his government was reviewing Sekaleshfar's visa "as we speak".

Immigration minister Peter Dutton earlier in the day said he was advised on Monday of Sekaleshfar's presence in Australia and his previous comments, and he would look at all the facts before making a decision.

"People who come to our country, regardless of what visa category they come on, they will abide by Australian law or their visa will be canceled and they will be deported from our country," Dutton said.

Sekaleshfar could not be reached for comment on Tuesday. He arrived at the IHIC just after nightfall to give his scheduled lecture, and declined to speak to media.

Calls and emails to the centre were not returned.

Sekaleshfar said on Monday that his comments in 2013 were made in the context of a lecture on Islamic law and homosexuality and should "not have been interpreted as a call for any Tom, Dick, or Harry to carry out a sentence wherever, whenever they like".

"In the context it was right," he said of the Michigan speech. "It wasn't inciting, nor saying to everyone to kill homosexuals, that it's open to everyone to do that, that's not the case."

He also said that in the speech he was referring to homosexual acts in public. "Even in an Islamic country, what they do in the privacy of their house, no one can say anything about," he said.

In his 2013 lecture, Sekaleshfar said: "There is nothing to be embarrassed about this. Death is the sentence."

"Islam doesn't accept people's faith to be compromised, to be threatened and it has to be taken seriously," he said. "With homosexuals it is the same."

Sekaleshfar, who gave a different lecture in Orlando in March, was on his second visit to Australia in as many years. He had said he had no plans to talk about homosexuality in this lecture series.

"I don't want the community in Australia to feel disappointed and thinking that I'm here to incite evil," he said before Turnbull's statement.

Additional reporting by Reuters.