Canberra sends asylum-seekers who try to enter the country by boat to camps on Nauru and PNG's Manus Island, with those found to be refugees barred from resettling in Australia.
They are instead relocated to third countries, or resettled elsewhere in PNG.
But the sudden withdrawal from PNG last week of American officials assessing the refugees sparked fears a deal with Washington to take them would not go ahead, particularly after reports earlier this year that US President Donald Trump had described it as "dumb".
"Our desire was obviously to have them off tomorrow, I want Manus Island to close, we're still going to maintain Nauru," Immigration Minister Peter Dutton told Sky News Australia.
"We have been caught up in the US process, they have a quota each year. It was 110,000 people they were taking in the refugee program under President Obama, but President Trump has reduced that to 50,000.
"Their year finishes in September, so we have been pushed into October in terms of when people will move."
The camps' conditions have been widely criticised by refugee advocates and medical professionals, who say some asylum-seekers suffer from mental health problems due to their prolonged detention.
Australians took part in numerous vigils Wednesday in support of those in detention and to mark four years since the offshore processing regime was set up by the previous Labor government.
More than 800 men are being held on Manus, and 370 men, women and children are detained on Nauru, according to Australian immigration data ending May 31.
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