Former BJP MLA Kuldeep Singh Sengar is an accused in the case.
The Supreme Court on Monday said that it wants "fair and speedy trial" in the Unnao rape case, in which ex-BJP MLA Kuldeep Singh Sengar is an accused.
The top court sought a report from the special judge Dharmesh Sharma, who is holding trial in cases related to the Unnao rape.
A bench of Justices Deepak Gupta and Aniruddha Bose sought the report from the trial court judge by September 6 about time needed for the completion of the trial.
"We want a fair trial but at the same time we also want a speedy trial in these cases," the bench said.
During the hearing, lawyers for Kuldeep Singh Sengar said that the CBI has not filed a chargesheet in the accident case.
The bench said that it would be better if it knows the views of the special judge on how much time was needed to complete the trial in these cases.
The bench listed the matter for Friday.
On August 19, the top court had granted CBI time till September 6 to complete the investigation into the road accident in which the Unnao rape survivor and her lawyer were critically injured and two of her aunts killed.
The top court, which had earlier given two weeks to the CBI to complete the probe, extended the time while noting that the probe agency has done "extensive investigation" in the case so far.
The CBI had told the top court that statements of rape survivor and her lawyer have not been recorded yet and it wants to analyse certain electronic evidence collected during the probe.
The court had also directed the Uttar Pradesh government to pay Rs 5 lakh to the lawyer, who is in a critical condition and undergoing treatment.
The court had taken exception to some public statements made by the family members of the rape survivor in the media and said it might help the accused during the trial of the case.
The top court had asked CBI to complete the investigation in the case within seven days, adding that the agency could avail additional seven days in exceptional circumstances, but in no case the time frame would be extended beyond a fortnight.
It had earlier ordered transfer of all the five related cases in the matter to Delhi but later modified its order putting in abeyance shifting of the accident case till the probe was completed.
The modification was done stating that due to shifting of the case, the local court was facing technical hurdle in passing orders of remand for the accused who are being arrested in course of the probe.
The court had said the order transferring the accident case "shall remain in abeyance for the period during which the said case remains under investigation, which we have stipulated in the order dated August 1, 2019, to be completed in a maximum period of 15 days, preferably within seven days. The order dated August 1, 2019, is modified accordingly".
In July this year, a truck had truck had rammed the Unnao survivor's car as she was travelling with her family and lawyer. Two of her aunts died in the road accident.
She was airlifted from a hospital in Lucknow and brought to the AIIMS for better care as she continued to be critical.