During a session at Kirribilli House in Sydney, Australian Prime Minister Malcolm Turnbull turned down the offer of assistance from the neighboring nation, saying that his government was "not taking it up at this time".
Videos and still pictures received by Reuters made by the United States.
"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.
"We have serious concerns about the welfare, safety and well-being of the roughly 600 men who remain in the accommodation compound, who are too frightened to leave", Colville said.
"The Australian government is not honest".
The remote Manus Island centre has been a key part of Australia's disputed immigration policy under which it refuses to allow asylum seekers arriving by boat to reach its shores, detaining them instead in PNG and Nauru in the South Pacific.
Her Australian counterpart, Malcolm Turnbull, however said Canberra preferred to work through an existing refugee swap deal he negotiated with former U.S. President Barack Obama a year ago.
"But also we have urged Australia and PNG to de-escalate the situation, resume basic services - water, electricity, medical services as well".
"Australia's policy of deterrence by rescuing people at sea, mistreating them and abandoning them has become a notion of cruelty".
A Manus Island refugee during the daily protest in the detention centre, 5-11-17.
"At the moment hundreds of naked men are lying around me", wrote Boochani.
Donald Trump called it a dumb deal but Malcolm Turnbull says the United States agreement to take 1250 refugees from Australia is his priority over New Zealand's offer to help 150. "They are starving and their bodies are getting weak".
The government has been facing growing pressure to accept the offer in recent days, with Opposition Leader Bill Shorten saying on Friday that Mr Turnbull should honour New Zealand's proposal and Liberal MP Kevin Andrews breaking ranks to join that call on Sunday.
Sudanese refugee Abdul Aziz Adam accuses Australia of abandoning them, and hopes New Zealand will offer them sanctuary.
"We want our offer to remain on the table so we can assist as much as we are able in expediting a resolution on this issue", she said.
Mr Turnbull will meet Donald Trump on the sidelines of the East Asia summit in the Philippines later this month and is facing calls to lobby for the U.S. president to speed up the resettlement process.