Doctors are trying to establish whether the one-year-old girls, born otherwise healthy in northwest Bangladesh, share the same brain, something that would vastly complicate the surgery.
"It would be a very delicate and sensitive surgery," said Ruhul Amin, chief paediatric surgeon at Bangabandhu Sheikh Mujib Medical University in the capital Dhaka.
"We're evaluating their condition and trying to contact experts across the world for opinions and help."
Their parents, both schoolteachers, came to Dhaka shortly after Rabia and Rukia were born, to seek medical help.
The parents did not even know they were having twins before the birth, with scans not revealing any abnormalities or indications of two children, said their father Rafiqul Islam.
"The doctor only said it was a baby with a bigger head," he told AFP.
The parents wanted to ensure "a better life" for their daughters -- despite the potentially fatal ramifications of the surgery.
"Most people come to visit my daughters -- either with sympathy or joke in their eyes -- which is intolerable to watch as a father," he said.
In rare cases, identical twins can be born with skin and internal organs fused together. About half are stillborn, and the survival rate is between five and 25 per cent.
In 2008 a baby born in Bangladesh with two heads died.
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