Women and Child Development Minister Kiran Walia dashed off a letter to Kumar citing the issues raised by counsellors of such centres at a meeting chaired by her and asked him to look into the grievances and take remedial measures.
Several CICs in Delhi provide counselling and legal services to sexual assault victims.
Walia said the CIC counsellors informed her that private vehicles sent by police don't have lady Constables, specially in relation to the fact that CIC counsels are mostly females.
"The lady Police officials are not available at night at various Police Stations so as to co-ordinate with CIC Counsellors and handle the rape victims, specially child victims sensitively," she said in the letter.
The communication comes in the wake of national outrage over the brutal gang-rape and assault on a 23-year-old paramedic student who died on Saturday at a Singapore hospital.
Walia also wanted all IOs handling rape victims need to be properly trained and sensitised for proper investigation.
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In the letter, she sought Kumar's "personal intervention to handle the cases promptly, efficiently and sensitively, specially on account of the fact that sexually assaulted victims have undergone traumatic situation."
"She also assured the counsellors that Mobile Vans will be made available by the Government which can be utilised by CICs for attending to the victims," an official release said.
The Minister also announced that shelter at two Homes for pregnant woman at Sarai Rohilla and Jahangir Puri would be provided to sexually assaulted victims, for immediate shelter in addition to existing facilities.
She also hoped that the sensitisation programme for police personnel dealing such cases would commence by next month.