The second phase of a marathon surgery is still underway and will go on till Friday morning.
"After 11 hours of surgery, the heads of the conjoined twins have been separated successfully. The health condition of the children is stable. After the separation, plastic surgery experts are now working on them. The operation procedure is likely to be complete by 9 or 10 am tomorrow", Odisha Health and Family Welfare minister Pratap Jena said in a statement.
A team of 30 doctors from departments including neurosurgery, neuro-anesthesia and pediatrics, were on the medical team that accomplished the successful operation.
The first phase of the surgery was done on August 28 when the doctors created venous bypass to separate the veins shared by the babies that returns blood to the heart from the brain.
The conjoined twins were admitted to AIIMS on July 13 from Milipada village in Kandhamal district of Odisha.
For the treatment of the twins, the Odisha government has sanctioned Rs. one crore from the Chief Minister's Relief Fund (CMRF).
(With PTI inputs)