Niue's Minister of Health Pokotoa Sipeli has confirmed the island's morgue is out of action and the government has asked the families of people who die to hold funerals within 24 hours.
At the weekend a woman was buried on the day she died, upsetting family who wanted to travel from New Zealand.
On Tuesday, a New Zealand tourist died at the Matavai Hotel and was put on that day's flight back to New Zealand.
Earlier the hospital manager, Bob Talagi, said the morgue could still be used but Mr Sipeli says that is not the case.
He says a unit has broken down, making it impossible to maintain temperatures and they are waiting for a part to be shipped from overseas.
"At the present moment it is not workable, the morgue is not working. One patient died last week - that's apart from the tourist. And we have gone back to our old ways - if a person dies today he has to be buried today."
Pokotoa Sipeli says this was the practice before the hospital was built.