By Alastair Wanklyn
Hospital staff pushed patients on trolleys into the street, where other patients sat in chairs.
Fire fighters aimed a jet of water at the building's burning upper floors.
Taiwan's state news agency said the fire broke out inside a hospice that was part of a large government-run hospital.
The nine people who died included patients, nurses and other caregivers. They suffered heart attacks, the news agency said. Other survivors were taken to nearby hospitals.
The fire began in the early hours on Monday. At that time of day, many of the staff were migrant workers covering the night shift. The family of one survivor was quoted praising the actions of an Indonesian nurse who carried patients out of the building on her back.
There's no confirmation how the fire began. The Taipei fire department is quoted saying it may have been an electrical fault in a life support system.
Officials said the bed mattresses appear to have burned too easily. But they added, the blaze was out in less than one hour. It appears the hospital's own fire prevention system was working. Images inside the building showed water sprinklers drenching wards.