Campaigners say the government in Canberra is "treating the men like animals" and are demanding they be allowed to resettle in Australia.
For four years, Australia has paid Papua New Guinea, its nearest neighbour, and Nauru to house asylum seekers who attempt to reach the Australian coast by boat.
Papua New Guinea security officials shouted at refugees who were fetching food from an Australian refugee camp, refugees at the center told Reuters.
"As I have said in New Zealand, we of course do not have the circumstances that Australia is operating under, but we also can not ignore the human face of what Australia is dealing with either", she said.
Australia has struggled to move the refugees to third countries such as Cambodia or PNG. They are Rohingya Muslims from Myanmar, Afghans, Iranians, Sri Lankans and other nationalities.
Amid reports of various abuses occurring at the camps, notably the one on Manus Island and another one on the Pacific island of Nauru, the policy has been vehemently criticized by the United Nations and human rights activists.
Around 500 of the men have still not had their asylum claims processed, he said. However, alternative accommodations are nowhere near ready, the United Nations refugee agency says.
Since the centre's closure last Tuesday, food, water, power and medical services were cut from the centre, where about 600 refugees are refusing to leave.
"Australia's policy of deterrence by rescuing people at sea, mistreating them and abandoning them has become a notion of cruelty".
New Zealand's newly elected Prime Minister Jacinda Ardern has reiterated an offer to take 150 refugees from offshore centres in her first meeting with Malcolm Turnbull.
"At the moment hundreds of naked men are lying around me", wrote Boochani.
Ms Ardern acknowledged on Sunday that the situation was becoming acute but understood Mr Turnbull's position to first pursue the United States deal because it would help substantially more people than New Zealand's small offer could.
New Zealand citizens are typically allowed to work and live in Australia, a pathway that Australia fears could be used by the refugees to move to Australia.
Ardern's relationship with Australia has been controversial since her election, with Foreign Minister Julie Bishop describing the 37-year-old New Zealand leader as "untrustworthy" after an MP from her own Labour Party delved into former deputy PM Barnaby Joyce's dual Kiwi citizenship status. "You can't keep political hostages".
"I acknowledge that, while New Zealand has not had to contend with these issues on our shores, it's hard to ignore the human face of this situation and nor should it be ignored", wrote Ardern.
Vice President Mike Pence said earlier this year the USA administration would honour the agreement.