The pair that remained were separated from the rest of the squad at their hotel on the Gold Coast – after indicating they would like to remain – and taken to a police facility in Brisbane, Immigration Minister Tony Burke said.
All will be fast-tracked to permanent residency, he said.
The offer to stay was reiterated to “most” of the remainder of the delegation at Sydney Airport before they were due to leave the country on Tuesday night, he continued.
Burke said a “very significant” police presence at Sydney Airport ensured players were separated from minders while they talked to officials one-on-one through a translator, and were given the chance to call family.
None of them chose to accept the offer to stay, Burke said, but he added that one person got on the plane “quite late” after conversations with family.
“That individual made their own decision,” Burke said – noting that there had been no pressure on them to take the flight.
He added a small number of the travelling group were not invited to stay – thought to be a reference to be Iranian government minders.
“There are some leaving Australia who I am glad are not in Australia,” he said.
The team arrived at Sydney Airport from the Gold Coast, where the Asia Cup is being held, on Tuesday evening. Members of the Australian-Iranian community gathered there to support them and to protest against them returning to Iran.
They said some members of the team had signalled for help.
Burke, quoted by the ABC, said Border Force officials had made “multiple representations to the team” before they left Sydney, “including private meetings”.
Local media reported that at least one person refused to board their later flight to Malaysia on their way back to Iran.
But some of the players – who were accompanied by chaperones – reportedly told reporters that they wanted to go back to Iran.
Australia’s humanitarian visa programme grants permanent protection to refugees and people in humanitarian need. Visa holders can live, work and study in the country.
