The petition filed before the Commission by Supreme Court advocate and human rights activist Radhakanta Tripathy said the Bhubaneswar institute did not have the infrastructure essential for the care and treatment of the twins, Jaga and Balia.
The NHRC has asked the All India Institute of Medical Sciences for a report on the matter.
"It is requested that an Action Taken Report be sent to the Commission within four weeks from the date of the receipt of this letter," NHRC said to the Director of AIIMS in a letter yesterday.
But the Odisha government was not "equipped" to treat the 31-month-old boys who underwent surgery at AIIMS here for the separation, it said.
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"The state government is not well equipped for their treatment in the state. Had that been the case, the operation could have been done in the state itself," Tripathy said in the recent petition.
It mentioned that the health condition of the twins, who have been staying at AIIMS since the operations along with their parents, had to improve further before they could be sent to Odisha.
"The facts and circumstances of the case also pose questions regarding the right to health and basic human rights of not only the kids but of the entire family," Tripathy said adding that unless the Commission intervenes, the "poor, uneducated ST family shall be deprived of justice".
The petition further pointed out that only Jaga was stable while Balia was not and that the twins parents had requested the Odisha government to ask the authorities at AIIMS to allow the children to stay in the hospital for some more months until they were fully fit to be shifted.
On February 26, a team of doctors from Odisha visited the twins to assess if they could be taken to AIIMS, Bhubaneswar, for follow up treatment.
Jaga and Balia were craniopagus conjoined twins -- joined at the head -- which doctors said was a very rare occurrence. They were successfully separated after a 21-hour-long surgery at AIIMS in New Delhi in October last year.
The final separation of the twin was performed by a team of around 30 specialists of AIIMSs neurosurgery, neuro-anaesthesia and plastic surgery departments on October 25.