Hearing on a petition filed by the girls' mother, the high court also sent notices to the three accused in the case.
Pointing out to contradictions in findings of the investigation reports, the girls' mother said that the autopsy report of the first child showed a mark of abuse but no investigation was conducted.
"Therefore, there is a need for an investigation and a reassessment of convictions. The appeals court also held that the POCSO court's verdict in the absence of evidence was not correct," the petition said.
On October 25, the POCSO court in Palakkad had acquitted the three accused -- V Madhu, Shibu and M Madhu -- in the case.
The high court had earlier dismissed a plea seeking a probe by the Central Bureau of Investigation (CBI).
The government has said that it would not oppose the family's petition against the POCSO court order.