The 28-month-old twins who are joined at the heads were taken to AIIMS on July 13 and a team of 40 doctors conducted the 20-hour long first surgery on them on August 28.
Jaga and Kalia are conjoined twins who are fused at the cranium.
"The health condition of Jaga-Kalia is fine after first surgery at the AIIMS in New Delhi, they are expected to go for the crucial second surgery after one-and-a-half months," Odisha Health Minister P K Jena said.
Odisha government has been funding the operation and deployed a health department employee to keep a tab on the health condition of the twins. A mass prayer was offered to Lord Jagannath by an organization at a local temple for the quick recovery of Jaga and Kalia.