A joint team of the police and Army laid a trap for Ishfaq Ahmad Padder in Tantray Pora village.
The terrorist was shot dead after he opened fire while trying to escape, the spokesman said.
The spokesman said Padder was involved in the brutal killing of 22-year-old Lt Fayaz in Shopian.
The newly-commissioned officer was abducted and killed by LeT terrorists in May, when he was attending a wedding of a relative.
Padder was also involved in robberies at the J-K Bank and Ellaquai Dehati Bank, besides a firing incident at the Yaripora police station, he said.
One AK-47 rifle, two magazines, 42 rounds and a pouch was seized from the gunned down terrorist.
'Burhan Wani or Lt Ummer Fayaz? Kashmiris have to decide'
Lt. Umar Fayaz's death may be a turning point in Kashmir
He is a hero: Top army commander meets slain Umar Fayaz's family
PHOTOS: Final farewell to army officer abducted and killed by terrorists
'Your killers will face the same fate'