It was the second self-immolation on Nauru in the past week. The first involved 23-year-old Iranian man Omid Masoumali. He died in a Brisbane hospital on Friday, after waiting more than 24 hours for medical evacuation to Australia.

Mr Dutton on Tuesday said the young woman had been airlifted to Australia and remained "in a very serious, critical condition".

'We can only hope for the best possible outcome ... It is of grave concern that this person would resort to such an extreme act of self-harm," he said.

He expressed anger at advocates and others "who are encouraging some of these people to behave in a certain way, believing that that pressure exerted on the Australian Government will see a change in our policy in relation to our border protection measures".

"These behaviours have intensified in recent times and as we see, they have turned to extreme acts with terrible consequences," Mr Dutton said.

"Advocates who proclaim to represent and support the interests of refugees and asylum seekers must frankly hear a clear message ... their activities and these behaviours must end."

Asked whether he believed self-harming refugees were mentally ill and desperate, rather than acting at the behest of advocates, Mr Dutton said they had "paid thousands of dollars to people smugglers to come to Australia and they haven't arrived in Australia. They are frustrated by that, I can understand that".

The Nauru government said refugee advocates, Australian politicians and human rights lawyers should "work with us in sending the message to refugees on Nauru that such drastic actions will not work, and to refrain from such protests".

"Refugee advocates must stop giving refugees and asylum seekers on Nauru false hope and stirring up these protests. Nauru cares deeply about each person who is a part of our refugee community ... locals have reached out to them and continue to consider them as our friends and neighbours," it said in a statement.

It is understood Hadon, believed to be aged between 19 and 22, received treatment at the Republic of Nauru Hospital on Monday night and arrived at the Royal Brisbane and Women's Hospital burns unit on Tuesday morning.

Refugee Action Coalition spokesman Ian Rintoul said the woman was "badly burnt [and that] all her clothes have been burnt off."

A former Australian teacher at Nauru, who once taught the victim, said she was "a kind woman, a good friend and would never harm anyone".

"Hadon used to come to English classes at night because she was too shy to come in the normal day classes," said the former teacher, who did not wish to be named.

"Gradually, in her gentle voice, she told us tragic pieces of her past in Somalia. She wanted to learn, she longed for a future.

Refugee advocates said she was one of three refugees returned to Nauru last week after travelling to Australia for medical treatment, following head injuries suffered in a motorbike accident on the island.

"This is another self-harm attempt that is [Immigration Minister] Peter Dutton's responsibility," Mr Rintoul said.

Labor's immigration spokesman Richard Marles, whose party supports the principle of offshore processing, said the latest self-immolation report was "deeply distressing".

"The Turnbull government's policy, focused only on deterrence with no feasible pathway to permanent migration in a resettlement country is leaving people desperate and without hope."

In a statement the United Nations refugee agency, UNHCR, said it was seeking more information about the latest incident.

"There is no doubt that the current policy of offshore processing and prolonged detention is immensely harmful," it said.

Greens immigration spokeswoman Senator Sarah Hanson-Young said there was "a tragedy unfolding on Nauru and we can't just stand by and watch".

"This young woman has been driven to despair by her treatment on the island. Malcolm Turnbull needs to intervene. The situation on Nauru is spiralling dangerously out of control," she said.

- With Bianca Hall and Jorge Branco