The directive was given during an hour-long meeting the Home Minister had with top security officials, including National Security Advisor Ajit Doval, besides others.
Sources said the Home Minister conveyed that the security forces must go after the instigators of the violence in Kashmir Valley and book them as they continue to disrupt normal life for 65 days after the killing of Hizbul Mujahideen militant Burhan Wani on September 8.
Singh said that normalcy should be brought back within a week and school and other educational institutions should function as students are worst sufferers during the prolonged turmoil, sources said.
Attempts should also be made to reopen shops and other commercial establishments which were shut completely, the Home Minister told the officials.
The Home Minister also reviewed the security situation in Jammu and Kashmir, where a policeman and three militants were killed in two separate incidents on Sunday.
One infiltration bid was foiled in Naugam sector, another in Tangdhar sector and the third one in Gurez sector.
The officials briefed the prevailing situation in Kashmir Valley as well as along the border and the steps taken to bring back normalcy in the state, official sources said.
So far, 75 people have lost their lives in the 65 days of turmoil.