"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.
Australia turned down on Sunday an offer to take 150 asylum seekers being held in an Australian-run detention center in Papua New Guinea, where United Nations officials have warned a humanitarian emergency is unfolding.
"Australia deny to give our fundamental rights such as water and food", said Adam.
"That is an offer that does remain on the table, so whilst it has not been taken up immediately, the prime minister thanked New Zealand for the offer, acknowledged it and it is something that still remains in place", she said.
The Australian government has not responded to Colville's comments.
"While [Australia] is not accepting refugees from Manus they have no right to reject New Zealand's offer".
The camps on Manus island and Nauru have been key parts of Australia's disputed "Sovereign Borders" immigration policy, under which it refuses to allow asylum seekers arriving by boat to reach its shores.
United Nations rights spokesman Rupert Colville told a news conference in Geneva on Friday about the "unfolding humanitarian emergency" in the Manus island center, where asylum seekers have been reported digging wells to try to find water. Among them are about 90 Rohingya Muslims from Myanmar, about 200 men from Iran, and others from Afghanistan, Somalia and Pakistan.
"We repeat our overall concerns about Australian offshore processing centres which are unsustainable, inhumane and contradictory to its human rights obligations", Colville said.
Food, running water and medical services were cut off by Australia four days ago. "They are starving and their bodies are getting weak".
Refugees had hoped Prime Minister Malcolm Turnbull would accept a longstanding New Zealand offer to resettle 150 people.
It was extended by his New Zealand counterpart Jacinda Ardern when the pair met in Sydney on Sunday.
The relocation of the men is designed as a temporary measure, allowing the United States time to complete vetting of asylum seekers as part of a refugee swap deal, agreed on past year, under which Australia will accept refugees from Central America.
Boochani said the New Zealand offer was "our best chance".
Australia entered into an agreement during Barack Obama's administration for about 1,200 of those detained to be resettled in the U.S.