He said giving asylum seekers New Zealand residence could give them a back-door into Australia.
The remaining men, who have been held on Manus for more than four years, insist they should be resettled in third countries and not simply transferred to another detention camp in PNG.
The camp, on a disused army base on Manus Island in Papua New Guinea, was declared closed on 31 October after a Supreme Court ruling that it was unconstitutional for Australia to house asylum seekers there.
Kurdish journalist and Iranian refugee Behrouz Boochani said police and immigration authorities had destroyed shelters built to provide shade and cover from the tropical sun and rain in a post on Twitter.
"For the mean time, the PNG and Australia government should supply food, water, electricity and medicines to the refugees and asylum seekers".
The men fear violent reprisals from the Manus island community if they move from the camp to three transit centers, pending possible resettlement to the United States.
Personnel from the PNG immigration department inside the detention centre.
Australia has used the Manus island center, and another on the tiny Pacific island of Nauru, to detain asylum seekers who try to reach its shores by boat.
"We're shutting them down for as long as we can.at least until the evening, to affect these people, and for these people to acknowledge and question what their Government is doing", Cullen said.
She's seeking another meeting with Turnbull to discuss New Zealand's offer to take 150 of the refugees and doesn't believe the Aussie PM sees it as a stunt.
"I see the human face of this, I see the need and the role New Zealand needs to play".
Another of the protestors, Anna Hush, said, "If Philip Ruddock claims to care about human rights, he should join us in calling on both Liberal and Labor to end offshore detention and bring the refugees here". No matter what label you put on it there is absolute need and there is harm being done, ' she said on Sunday. "I think it's clear that we don't think what's happening there is acceptable, that's why the offer is there".