The United Nations' refugee agency is disappointed Australia has repealed laws which made it easier to secure medical evacuations.
The UNHCR said the medevac mechanism had "proven to be a timely, effective and often life-saving safeguard".
"After more than six years of uncertainty regarding solutions, UNHCR is extremely concerned that the health situation of asylum seekers and refugees will continue to deteriorate," the agency said in a statement on Thursday.
It urged the Morrison government to continue to use existing mechanisms "in a good faith effort to evacuate individuals in need of urgent medical treatment".
"As Australia retains responsibility for people forcibly transferred under its offshore arrangements, UNHCR urges the government of Australia to find appropriate solutions, including taking up the longstanding offer by New Zealand to resettle refugees and to prevent further harm."
Earlier, Prime Minister Scott Morrison signalled the door was open to accepting New Zealand's longstanding offer to resettle refugees, after securing support from crossbench senator Jacqui Lambie to repeal the medevac laws.
The prime minister insists no deal was done to win over Senator Lambie.
But it is believed she was assured the government would pursue the New Zealand option, once a refugee resettlement deal with the United States had concluded.
Chief government negotiator Mathias Cormann said Senator Lambie was provided detailed briefings and classified information during negotiations on repealing the medevac laws.
"At the end of that process Senator Lambie, by her own words, was satisfied that the repeal of the bad medevac laws was warranted," he told reporters.
After scrapping the medevac laws, the prime minister confirmed his goal was to resettle refugees being held offshore.
"We've always been very aware of the New Zealand government's offer," he told reporters.
"The government will continue to implement our policies as we've set them out and as we've decided to do as a government. That's what we'll do."
Mr Morrison also said legislation which failed under the Turnbull government, to ban refugees from New Zealand coming to Australia, remained coalition policy.
The government has occasionally floated the idea of accepting the resettlement deal if the visa ban is in place.
Home Affairs Minister Peter Dutton talked down the prospect of taking up the New Zealand offer any time soon.
"There is no sense pulling 100 people off Nauru if the next day you've created a pull factor and a boat with 150 people arrive ... we have to be sensible about it," he told 2GB radio.
While talking about resettlement options, the prime minister made repeated reference to Nauru but was silent on the asylum seekers held in Papua New Guinea.
There are about 460 people detained across the two countries.
Many of the men in PNG have not gained refugee status and may not be accepted by New Zealand or other countries.
New Zealand Prime Minister Jacinda Ardern has confirmed its longstanding offer to resettle 150 refugees per year from Australia's offshore processing centres remains on the table.
"The ball is obviously in Australia's court," she told Sky News.