Ladan and Laleh Bijani will be buried in the village of Lohrasb, 680 miles southwest of Tehran, on Saturday, the parents said.
"We are not prepared for the burial today. We've been overwhelmed by hundreds of people coming to pay their respects and we were not able to prepare for a respectable burial ceremony, one which they deserve," said their father, Dadollah Bijani.
The coffins were driven from the capital, Tehran, in two Red Crescent Society ambulances accompanied by dozens of vehicles.
Hundreds visited the bereaved parents at the modest family home. In line with Muslim custom, women were separated from men in different halls.
Villagers placed photos of the twins and placards expressing condolences on lamp posts and buildings in Lohrasb, while workers prepared their grave sites.
The deaths of the two women Tuesday after 54-hour surgery in Singapore caused sadness around the world but particularly in Iran, which had watched and admired the courage of the girls as they grew up attached by their heads.
People halted work and parked their cars to cry when normal programming on radio and television were interrupted to announce the news. President Mohammad Khatami also paid tribute to the twins' resolve and patience.
The bodies were flown from Singapore on Thursday and were given a reception normally reserved for slain soldiers and prominent figures.
On Friday, hundreds paid their respects at Tehran's Grand Mosque, where the coffins were laid out before they were taken to Firouzabad — a town near Lohrasb — where the bodies were stored in a morgue.
The twins had left Iran seven months ago to prepare for the operation in Singapore.
The sisters, who had been adamant in wanting to be separated despite the risks of the operation, died within 90 minutes of each other after doctors separated them but failed to control the bleeding in the unprecedented surgery.
It was the first time surgeons had tried to separate adults joined at the head. The surgery had been performed successfully on infants, whose brains can more easily recover.