Sisters Tofa and Tahura, who were born conjoined at the spine and rectum, underwent a gruelling nine hours in surgery under the care of two dozen doctors.
"It is the first time we have successfully separated critically conjoined twins in Bangladesh," paediatric surgeon Abdul Hanif of Dhaka Medical College Hospital told AFP.
"It's a groundbreaking operation in our medical history," Hanif said, adding that it had been "extremely complex".
Almost all Bangladeshi conjoined twins fail to survive their infant years, the surgeon said.
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Tofa and Tahura will need at least two further operations to restructure their internal organs, Hanif added.
The surgery had been "100 percent successful" but the twins would remain in intensive care for at least a week to ensure no infections developed, said surgery coordinator Shahnoor Islam.
Born to poor farmers, the sisters -- who do not use a surname -- were brought to Dhaka a month ago from northern Gaibandha district, 260 kilometres (160 miles) from the capital.
"I held my daughters to feed them. They were responding very spontaneously," the mother of three said.
"My five-year-old son is very excited knowing he might now be able to play with his sisters. He cried to go inside the intensive care unit to see them but the doctors won't allow him," she said, adding that there are still fears of infections.
The surgeons said the next few days would be critical for the twins as the surgical wounds need to heal and the babies need more procedures to be able to live independently.
"We went to local clinics but nobody could provide any solution. We went to the district civil surgeon who advised us to go to Dhaka. He paid for the trip and even rented an ambulance for us," Begum said.
The hospital paid the cost of the operation. Begum has vowed to send her daughters to Islamic seminaries if they grew up healthy.
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