The militants, presumed to be two in number, had entered the Delhi Public School located close to the Srinagar-Jammu National Highway after carrying out the attack in the nearby Pantha Chowk in which one CRPF officer was killed and a constable injured.
The attack on the road opening party of the CRPF took place in high security zone located less than a kilometre away from the headquarter of the Srinagar-based Army Corps.
An offensive to flush out the militants was launched this morning, a police official said.
"The exchange of fire between security forces and militants began at around 3.40 am and is going on intermittently," he said.
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"Two Army personnel were injured in the gunbattle today," the official said. He said the injured have been taken to a hospital.
The building where the militants are holed up has been identified, Jammu and Kashmir's Director General of Police S P Vaid said.
"As per the information, there are two probably," he said.
He said the operation was getting prolonged as the security forces want to avoid collateral damage.
"We will have room intervention done and get these terrorists eliminated, but with minimum collateral damage," he told reporters.
"We want to ensure that the (school) building is safe, because the enemy has a nefarious design that the school buildings are destroyed and children have nothing to study and ultimately abandon their studies, which we will ensure that no such thing happens," Vaid told reporters here.
On the operation getting prolonged, the state police chief said, "There are 36 rooms, the building is huge. So, it has to be searched floor by floor, room by room."
Asked whether the security forces were using drones cameras and other hi-tech gadgets to help flush out the militants, the top cop said "we will use whatever equipment we have".
The authorities have imposed restrictions under section 144 CrPc from Ram Munshibagh to Sempora stretch of the national highway as a precautionary measure to avoid protests near the encounter site.