"We call on the Australian government. who interned the men in the first place to immediately provide protection, food, water and other basic services", United Nations rights spokesperson Rupert Colville told a news briefing.
Since it was opened, the Australian-run camp on Manus Island has been under near constant scrutiny and criticism by human rights groups about everything from the poor state of its basic infrastructure to allegations of torture and mismanagement, astonishing rates of trauma and mental illness, and six deaths including one murder by a local resident.
Noting that all migrants, including refugees and asylum-seekers have a right to a safe and secure environment, a right to an adequate standard of living and to participate in the decision-making process that is affecting their future, Colville said: "Human dignity should be ensured throughout the entire processing of their asylum claims".
Nicole Judge, who worked for the Salvation Army at the centre, said she had advocated for closing Manus Island but didn't want refugees and asylum seekers to be left there to suffer.
The two men described their situation, in which they said they found themselves without basic provisions or medical supplies following the closure of the off-shore detention centre.
Opposition Leader Bill Shorten said Prime Minister Malcolm Turnbull should seriously consider New Zealand's offer.
Hundreds of asylum-seekers in an Australian offshore detention camp on Papua New Guinea are hunkering down and refusing to leave.More news: Arsenal's Santi Cazorla opens up about career-threatening injury
Australia has an obligation to do so under global human rights law and the 1951 UN Refugee Convention, he said.
A refugee advocate holds a placard as she participates in a protest in central Sydney, against the treatment of asylum seekers in detention centres located in Nauru and on Manus Island, on October 15.
Australia scheduled the Manus camp for closure after Papua New Guinea's Supreme Court ruled previous year that the detention center was unconstitutional, as it violated the detainees right of personal liberty.
New Zealand's prime minister on Friday repeated her country's offer to take up to 150 refugees from an Australian immigration camp in Papua New Guinea, where more than 600 weakened men are continuing a standoff with authorities. "We have been here for more than four years".
Behrouz Boochani, an Iranian refugee at the Manus center, also said he wanted Steinmeier to press the government to come up with a "humane solution". "They are starving and their bodies are getting weak". "You can't keep political hostages".
"It's a challenging situation for Australia, they face issues that we don't in New Zealand", he said. Lives lived in fear & despair.
Australia entered into an agreement during Barack Obama's administration for about 1,200 of those detained to be resettled in the U.S.