A M-4 Carbine, used for carrying out sniper attacks on security forces, was also seized from the encounter site, officials said.
Two bodies were recovered after a day-long encounter that broke in Chaanketaar village of Tral in Pulwama district, they said. The body of one more terrorist was expected to be retrieved from the rubble, they said.
The intelligence inputs as well as the material seized from the encounter site showed that the terrorists belonged to JeM, they added.
The police had not officially identified the bodies, but officers speaking on the condition of anonymity said Haider was among those killed in the encounter.
A statement and video purportedly shared by Jaish-e-Mohammed on social media identified one of the killed terrorists as Haider.
It also claimed that he was heading sniper attacks in Kashmir for quite sometime.
The security forces also recovered M-4 Carbine rifle from the encounter site which was used by the group to carry out sniper attacks on security forces, they said.
Last week, an Army jawan and a Seema Shashtra Bal personnel were killed in the sniper attacks in Tral area.