The girls had hanged themselves in the bathroom of the Nari Niketan on June 25 in 2013.
National Human Rights Commission (NHRC) has asked the Chief Secretary of the state to submit the compliance report along with proof of payment within six weeks.
Earlier, in response to the show cause notice of the Commission, Haryana government had contended that the functioning of Nari Niketan was being monitored regularly by the district administration for the safety of inmates.
"After consideration of the response of the state government, Justice D Murugesan, member of the Commission, has observed that it is the statutory duty of the state and its functionaries to ensure the safety of the detainees during their custody.
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"The government has the absolute right to hold persons for offences against it, but it also has a co-relative duty to protect them against assault or injury from any quarter while in custody. Thus, the management of the 'State After Care Centre' failed to perform its duty as per law for which the state was liable to compensate to the next of kin of the deceased," the Commission said.
The girl from Kaithal was brought to the Nari Niketan on June 17, 2013 while the girl from Mahendergarh was lodged in the shelter home on June 22, 2013 on the directions of a court after being caught by police on complaints that they had run away from their respective home with some men of their choice.
On June 23, 2013, both escaped from the Nari Niketan but were traced and brought back. They both committed suicide two days later.