Seven people, including two soldiers, died in an encounter on Sunday in Kulgam, 70 km south of Srinagar.
"First we tried to convince them to surrender with the help of locals and family members", Patil said to The New York Times.
In fresh clashes between irate crowds and security forces, at least, half a dozen people were injured in Palhallan and Keemwa areas.
The search operations was still in progress as security forces suspect that some militants might have managed to escape to nearby areas, the official said.
He said they had outstanding criminal charges, including murder and stealing arms from security forces. Two of their soldiers were killed in the encounter and they took their revenge by firing at and killing ordinary people who were staging protests.
Left wins presidency in new blow to Merkel
Opposition parties, The Greens and the Free Democratic Party (FDP), also backed Steinmeier as the country's next president. Since Mr Schulz took over the candidacy in late January, the SPD has risen sharply in the opinion polls.
Police said two militants belonged to the Lashkar-e-Taiba and the other two to the Hizbul Mujahideen.
All shops and commercial establishments remained closed in Srinagar.
Meanwhile curfew like restrictions have been imposed in parts of south Kashmir where situation remains tense following the killing of civilians and militants in the Kulgam encounter yesterday. A civilian was also killed in the shootout between militants and security forces.
Strikes in the valley started from February 9 on the death anniversary of Afzal Guru, followed by "UN office chalo" campaign on 10th and anniversary of JKLF founder Maqbool Bhat on 11th and now another strike call by separatists on Monday. He also slammed the Indian Army for using innocent civilians as human shields "to avoid casualties".