Iranian Mohammad Abdi, who was granted residency in February 2011 with his wife and first son, was arrested last month, provisionally charged, and is in custody while the police investigation continues.

Their two-year-old second son was born in Australia, after the family returned to Australia as UN-certified refugees, and is an Australian citizen, according to his mother. The couple had first arrived by boat in 2009, but feeling homesick, they returned home only to be persecuted after converting to Christianity.

The immigration minister has the discretion to revoke the boy's citizenship and order deportation under Section 34 of the Australian Citizenship Act, in the public interest.

"It's extraordinary that a child born to asylum-seekers has no right of citizenship but that's what the law says," said Asylum Seeker Resource Centre chief executive Kon Karapanagiotidis.

The department confirmed Mr Abdi's visa had been cancelled, along with those of his wife, who claims they are separated, and the children. As people now unlawfully in Australia, the wife and sons were liable to detention and removal from the country, a spokesperson said.

The family's visa cancellations were "consequential" on the department's determination that 36-year-old Mr Abdi's return to Australia would be "a risk to the health safety or good order of the Australian community".