Based on information regarding the presence of militants, security forces started a search in Hakoora area of Anantnag district.
"The hiding militants tried to break the cordon and opened fire upon the joint team".
Khan said the third militant was apparently a foreigner and his identity is being ascertained.
He said Fazili, who was a BTech student and had joined militancy in August past year, and Owais were affiliated with Tehreek-ul-Mujahideen.
"In the process arms and ammunition which include AK 47 rifles, pistols, hand grenades etc were recovered from the encounter site".
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Mr Skripal was convicted in 2006 of passing state secrets to MI6 before being given refuge in the United Kingdom as part of a spy swap.
Al Jazeera's Priyanka Gupta reports.
Before joining the militant ranks, Fazli was pursuing a B.Tech course in Baba Ghulam Shah Badshah University in Rajouri district.
Owais, who was also a BTech student, had joined course in Electronics and Communication from BGSBU in November 2017.
Meanwhile, thousands of people defying curfew and other restrictions reached Soura and Kokernag on motorcycles and on foot to participate in the funerals of the martyred youth. Eesa Fazli hailed from Srinagar while Syed Owais was from Kokernag.
Fearing protests in Srinagar, authorities ordered the closure of all educational institutions in the city, while restrictions were imposed in sensitive areas.
Terror outfit Islamic State (IS) had claimed responsibility for the killing of constable Yatoo on their official channel. The markets in Ganderbal and Kangan towns remained closed for the second day while the students of Degree College Ganderbal and Gandhi College Babdemb Srinagar assembled outside the college gate and staged a protest.