The United Nations has called on Australia to immediately evacuate its offshore detention centres to prevent an unfolding health crisis.

Doctors from Médecins Sans Frontières (MSF) were ejected from Nauru on Wednesday and the UN high commissioner for refugees has warned that many asylum seekers who have attempted self-harm or have critical health issues now have no access to medical care.

Catherine Stubberfield, a spokeswoman for the UNHCR in Canberra, said healthcare was “collapsing” at the centres.

She said a pre-teenage girl doused herself with petrol in a suicide attempt last month, and remained on Nauru despite a doctor’s advice to have her evacuated.

UNHCR does not agree with the government of Australia’s assertion Catherine Stubberfield

She also said many asylum seekers in Papua New Guinea had attempted self-harm or suicide last month, and others were suffering “acute” physical and mental health issues but had not been treated by doctors.

On Thursday, MSF called for an immediate humanitarian evacuation of offshore detainees. It said there had been 78 cases of attempted suicide and self-harm in Nauru over the past year.

Speaking on Friday, Stubberfield said Australia had to face the responsibility of its offshore detention camps because it had designed, paid for and set up the system.

“UNHCR does not agree with the government of Australia’s assertion that such cases are solely ‘matters for Papua New Guinea and Nauru’,” she said. “Australia [has] simultaneously designed, financed and managed the system.”

She urged the Australian government to take up New Zealand’s offer to accept some of those held in detention.

About 1,420 people are being held in PNG and Nauru, and 500 have been transferred to Australia for medical reasons. The UNCHR’s monitoring suggests that figure is “significantly lower” than the number of refugees in need of care.

“In September this year more refugees and asylum seekers had to be medically evacuated from Nauru to Australia than in the preceding two years combined,” Stubberfield said. “[But] this reflects the longstanding poor healthcare situation and a recent worsening of conditions, rather than any moderating of stance.

“In Papua New Guinea there have been no re-transfers to Australia this year. This is despite a clear and urgent imperative for medical evacuation.”

Twelve people have died in immigration detention on Nauru and Manus Island since 2014.

The Australian government contracts International Health and Medical Services and Pacific International Hospital to provide medical aid at Nauru and PNG respectively but the UN described their services as “limited”.

It also said the local healthcare systems were “under-resourced and understaffed in both countries”.

The Department of Home Affairs said in a statement that it took refugee health and welfare “seriously”.

“Through the Australian government’s contracted health services provider, general practitioner, nursing and mental healthcare clinics are open seven days a week. There is also after-hours medical staffing to respond to after-hours medical emergencies,” it said.

“There are 65 contracted health professionals, including 33 mental health professionals providing services to transferees on Nauru. All transferees on Nauru are free to move around the island; they are not in detention.”

In September, Guardian Australia revealed that the government spent more than $320,000 last financial year challenging applications for medical transfers from Nauru and Manus Island.