The court has ordered that the trial should be completed within 45 days.
A Bench headed by Chief Justice Ranjan Gogoi also awarded Rs 25 lakh as compensation to the victim.
The court has granted two weeks to conclude the investigation into the truck-car accident of Sunday which left the rape victim and her lawyer in critical condition and her two aunts dead.
The Rae Bareli CRPF Commandment has been asked to provide adequate security to the victim's family which has alleged threats from BJP MLA Kuldeep Singh Sengar and his henchmen.
The court asked the Uttar Pradesh government to say whether the uncle of the victim should be shifted to Tihar Jail from a Rae Bareli Jail.
The Bench will continue the hearing on Friday to know if its directions had been carried out.
The judges also said that if medically fit, the victim and her lawyer will be shifted out of Lucknow for advance treatment in Delhi.
The court has sought the views of the family on the issue.
The Supreme Court has expanded its suo moto registered PIL on the steps to curb child rape cases and included in it the issue of compensation and protection to the Unnao rape victim.
Chief Justice Gogoi on Wednesday took suo moto cognisance of a letter written by the family of the victim alleging threats from Kuldeep Sengar's men.
On Sunday, the rape victim, who had accused Sengar of raping her in 2017, was travelling to Rae Bareli with her lawyer Mahendra Singh and two aunts when a truck being driven on the wrong side hit them.
The rape victim and her lawyer are on life support. Of the two aunts killed in the accident, one was a witness to the crime.
( With inputs from IANS )