According to the security sources both militants have been killed.
Three army personnel, including a captain, have been injured in the encounter. However, their condition was stable, authorities said.
According to police, the gunfight started after midnight between the militants holed up inside the Delhi Public School (DPS) complex here and the security forces in Pantha Chowk area of Srinagar.
S.P. Vaid, Director General of Police (DGP) told reporters two militants are holed up inside the DPS complex.
The militants on Saturday attacked a Central Reserve Police Force (CRPF) vehicle on the Srinagar-Jammu national highway.
A Sub-Inspector of the CRPF was killed and two troopers injured in the attack after which the militants entered the DPS complex. Security forces immediately surrounded the school complex to prevent the militants from escaping.
The Lashkar-e-Taiba (LeT) militant outfit owned responsibility for the attack.
District Magistrate of Srinagar, Farooq Ahmad Lone on Saturday imposed restrictions on the stretch of Srinagar-Jammu national highway between Ram Munshibagh and Sempora.
Mobile internet services (3G/4G) were also suspended in the Kashmir Valley to prevent the spread of rumours.
The speed of landline broadband connections has also been brought down.
Also, in a freak accident, the service rifle of a policeman went off at the site of the militant attack on Saturday.
Two persons including a CRPF trooper and a policeman were injured in the freak accident.