The Turnbull government has signed a deal to send refugees on Nauru who need urgent medical care to Taiwan, in an undisclosed arrangement aimed at stopping them from applying to stay in Australia after being treated in local hospitals.

Fairfax Media can reveal Australia signed a memorandum of understanding with Taiwan - which is not a signatory to the 1951 Refugee Convention - in September last year that has so far seen about five refugees flown 5500 kilometres to the capital Taipei for high-level care.

Refugees on Nauru who need urgent medical treatment are being sent to Taipei in Taiwan instead of Australia.

The previously undisclosed deal has prompted lawyers to warn that medical care is being dictated by the political imperative of avoiding having refugees on Nauru reach Australia, where they can access its court system.

In recent months, a 55-year-old Iranian woman in need of critical heart surgery has been among the people treated in Taiwan and then returned to Nauru. A 63-year-old Afghan man who is reportedly dying of lung cancer is refusing to move to Taiwan for palliative care, demanding instead to come to Australia.