The 42-year-old man, known by the pseudonym Abdullah, was taken to the Nauru Hospital on August 29 after suffering severe pain in his chest and numbness in his left arm.

Abdullah said the pain had him writhing "like a snake" on his bed in his home, a converted shipping container, before he was taken to hospital by ambulance.

He was told he needed to be flown to Australia or Papua New Guinea for treatment, but discharged himself because there was no one else to care for his sons, aged 12 and 13.

One of his sons has mental health problems and a history of self-harm. The children's mother died before Abdullah and his children travelled to Christmas Island and were transferred to Nauru in 2013.

Abdullah said he also chose to leave the hospital because he found the conditions intolerable. He slept in a corridor because of an overwhelming smell in a room he was sharing with another man.

After initially being told he would have to leave his children on Nauru if he was flown for treatment, he was later assured they could travel with him. That was about two weeks ago. He last saw a doctor two days ago. "I am still waiting," he said.

Australian-based cardiologist Clare Arnott, for Doctors for Refugees, said Abdullah's medical records suggested it was likely he had suffered a heart attack and his life would be in danger if not properly treated.

"The risks of inadequate treatment in this case are great – from irreversible myocardial damage to repeat infarction, life-threatening arrhythmia and death," Dr Arnott said.

"I would certainly recommend urgent transfer to a facility that can provide specialist cardiology care, echocardiography and coronary angiography with intervention."

Abdullah said that  he was encouraged by officials based in Nauru to write a will leaving his children in the care of the Nauruan government in the event of his death, but refused. The will he signed said he wanted his children to be raised in Australia.

The Australian government has said no refugees who arrived in Australia by boat will be allowed to settle in the country. Refugees transferred to Australia for medical treatment are returned to Nauru once they have recovered.

A spokesman for Immigration Minister Peter Dutton referred questions to the Immigration and Border Protection Department. A department spokesman said it could not provide specific details on the medical treatment of individuals.

The spokesman said Australia provided significant support to Nauru to provide welfare and health services for refugees, and that people requiring treatment not available on Nauru may be transferred to Papua New Guinea to get the care they needed.

"Where appropriate medical services are not available in a regional processing country, transfer to Australia may be considered," he said.

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