On Sunday, the young woman, her paternal and maternal aunts and her advocate were travelling towards Rae Bareli in a car when it was hit by a truck.
Both the aunts succumbed to their injuries while the others were transferred to a trauma centre in Lucknow. The rape victim and the lawyer are in critical condition.
NCW Chairperson Rekha Sharma said in a letter to DGP O.P. Singh: "We have taken suo moto cognizance of media reports... It is requested to ensure fair and speedy probe into the matter and take action for the crime committed.
"The Commission is seriously concerned about the unfortunate incident. Considering the gravity of the matter, it is requested to ensure absolutely free, fair and speedy investigation into the matter and take action," the NCW said.
Meanwhile, Delhi Commission for Women (DCW) Chairman Swati Maliwal on Monday visited the Unnao rape victim and said she will assist her in shifting her to Delhi from the King George Medical University (KGMU) in Lucknow.
Maliwal said: "The doctor said the girl and lawyer are in critical condition. They also feel that the injured should be shifted to a top Delhi hospital by an air ambulance. The girl's family also wants her to be shifted to Delhi. I am in touch with some hospitals and we are ready to take up the responsibility."
Several other political leaders also reached the hospital to express solidarity with the rape victim and the lawyer.
( With inputs from IANS )