Peter Dutton did not disclose a timeline on closing Manus Island detention centre in an interview with Sky News on Tuesday evening.
"It will take some time," he said.
The immigration minister did not clarify whether it would take months or years, after being pressed for an answer on the length of time, saying the Australian government would continue to "work with our partners in PNG".
Papua New Guinea's Prime Minister Peter O’Neill announced earlier in the day that the Australian and Papua New Guinean governments had agreed to close the offshore processing centre.
"Both Papua New Guinea and Australia are in agreement that the centre is to be closed," Mr O'Neill said in a statement on Tuesday.
The announcement came after Mr Dutton met with Mr O'Neill on Tuesday in Port Moresby.
"The Supreme Court has delivered its ruling and our government is complying with this decision," Mr O'Neill said.
He did not outline how the centre would be closed and where asylum seekers would be relocated.
"It is important that this process is not rushed out but carried out in a careful manner," he said.
In a statement, Peter Dutton reinforced the Coalition's policy that it would not assist asylum seekers to resettle on Australia's shores.
"It has been the longstanding position of this government to work with PNG to close Manus and support those people as they transition into PNG or return to their country of origin."
The Australian government is also considering third-country arrangements, he told Sky News. However he did not specify what countries were being considered.
Human rights organisations remain skeptical
Amnesty International Australia criticised the announcement for failing to deliver a deadline.
“Amnesty International calls on Australian Minister for Immigration and Border Protection, Peter Dutton, to urgently confirm the timeframe by which it will close the detention centre and safely settle refugees in Australia," Anna Neistat, Amnesty International’s Senior Director for Research said.
"We must not forget that the Government set up a system of deliberate abuse of and cruelty towards almost two thousand men, women and children who are simply looking for a safe place to rebuild their lives."
