Kumar visited the family of Head Constable Mushtaq Ahmad at Arigam in Pulwama district and expressed condolences to the bereaved, a police spokesman said.
He said that the families of the cops are not alone in this hour of grief as the "whole police parivar is sharing their grief".
Mushtaq Ahmad was killed in a militant attack at Amshipora in Shopian district along with Constable Shabir Hussain and Constable Nisar Ahmad yesterday.
The DGP was accompanied by IGP Kashmir Zone S J M Gillani and SSP Pulwama Tejinder Singh.
Head Constable Mushtaq Ahmad is survived by elderly parents, wife and two minor children.