Acting on credible inputs about the presence of militants in Achabal area of the south Kashmir district, security forces launched a cordon and search operation and the hiding militants opened fire.
The bodies were retrieved from the site of the encounter and handed over to the legal heirs.
While the slain terrorists are yet to be identified, the encouinter is still underway.
Four Counter-Terrorism Department personnel were injured int he operation in Balochistan province from where a huge cache of ammunition, explosives and weapons were also recovered.
Defence Ministry spokesman Colonel Rajesh Kalia said the militants were killed in an encounter in Nowgam, on the outskirts of Srinagar city.
The two militants were killed in the encounter, which began on Friday morning when security forces launched a search operation in Babagund area of Kupwara.
As the security men were conducting searches, they came under heavy fire from militants hiding in the area. The fire was returned by the troops, triggering an encounter.
Incriminating material, including arms and ammunition were recovered from the encounter site in Gopalpora village of Chadoora area, an officer said.
Waseem is the third PhD scholar to be killed in an encounter in J&K after Manan Wani, who was killed last November, and Sabzar.
The Taliban commander had masterminded last year's powerful bomb blast in the restive Khyber Pakhtunkhwa province in which at least 31 people including three Sikhs were killed.
Army foils infiltration bid along LoC, three militants killed in Macchil sector of Jammu and Kashmir
Troops noticed suspicious movement along the LoC in Macchil sector in Kupwara district and challenged the infiltrators.
Clashes broke out Monday in Soura area of Srinagar as scores of youths marched to attend the funeral of Essa Fazili, one of the three militants killed in a gunfight