Under that deal, up to 1,250 asylum seekers could be sent to the United States and Australia will in turn accept refugees from Central America.
Australia will continue to manage the refugee crisis which is teetering on a humanitarian crisis on Manus Island's detention center after declining New Zealand's offer to host 150 refugees.
The local boat owner was later released.
New Zealand's offer to accept 150 refugees from Manus Island and Nauru was waved away, with Turnbull saying his government had to first consider its refugee-swap deal with the US.
"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.
Those inside claim they will be attacked by PNG locals if they move to an alternative unfenced accommodation at nearby Lorengau.
Colville joined the UN High Commissioner for Refugees (UNHCR) in warning of an "unfolding humanitarian emergency" in the centre where asylum seekers began digging wells on Thursday to try to find water as their food supplies dwindled. And we on Manus Island we have lost hope.
"We repeat our overall concerns about Australian offshore processing centres which are unsustainable, inhumane and contradictory to its human rights obligations", Colville said.
Ms Ardern said Australia maintains there are alternate sites where refugees can get electricity and water, "but that for safety reasons some of those refugees have refused to move".More news: Carter Page met with Russian official during 2016 trip to Moscow
"As the prime minister at the time I honoured the arrangement of the previous government but once the processing was completed, my government put a stop to this so-called Pacific Solution", Sir Michael said in his statement, adding any resettlement needs support services.
New Zealand-born actor Russell Crowe is angry Australia hasn't considered NZ's refugee offer. "They are starving and their bodies are getting weak".
Ms Ardern revealed she did suggest to Mr Turnbull to take up both offers from New Zealand and the United States, but she said Mr Turnbull wanted to make sure the deal with the U.S. "actually comes to fruition".
"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", Ardern wrote.
"New Zealand isn't in the situation Australia is in".
The government is reluctant to resettle refugees in New Zealand because it believes that will encourage asylum seekers to again attempt to reach Australia by boat.
"Australia blocking but has no right to say no", he wrote on Twitter.
"We have an arrangement with the United States where a substantial number - 1250 - can, subject to the USA rigours vetting, be resettled in the United States", he said.