In his order to Principal Secretary (Home) Manoj Parida, Delhi Home Minister Satyendar Jain has asked him to ensure that such cases were given top priority for the earliest completion of prosecution.
The Delhi government's move comes at a time when there is a public outcry over Kathua and Unnao rape cases in the country.
"Keeping in view the ever-increasing incidents of crimes against women/girl/Protection of Children from Sexual Offences Act (POCSO) offences, all such cases referred for forensic examination need to be attended urgently for earliest completion of prosecution.
"Accordingly, please ensure that such cases are given top priority and forensic examination is completed within a month," Mr Jain said in the order.
An official said that the government was currently ascertaining the number of pending cases where forensic examination was yet to be completed.
While vowing to take the legislative measure during the next assembly session, Mr Kejriwal had also said he would also set up fast-track courts to complete the trial of the cases of crime against women in six months.
The official said that the home department of the government had started working on preparing a proposed Bill to amend the IPC and the CrPC.
The chief minister had also urged citizens to take a day off and support the DCW chief Swati Maliwal in her indefinite hunger strike at Rajghat, demanding stringent laws and the death penalty for rapists.