As morning prayers ended in nearby mosques in the capital Srinagar on Thursday, renewed gunfire from the fighters' hideout killed an army major and injured two other soldiers, an army spokesman said.
He said one of the two fighters was killed when the army fired back.
"The firing from the militant side has stopped and we are closing in to find out if the second militant is also dead," he said.
The two fighters attacked a camp of the Central Reserve Police Force on Tuesday evening killing a policeman and injuring three others. They then fled to a nearby building which police on Wednesday blasted with rockets and mortars.
In the ensuing fire fight, another four members of the security forces and a civilian were wounded, police said. Reports suggested the fighters had got into a neighbouring building during the night.
"I have never heard such deafening blasts"
Residents reported heavy firing and ground-shaking blasts since early morning.
"I have never heard such deafening blasts," resident Abd al-Aziz said. His family has been unable to leave the house since the army sealed off the area on Tuesday.
The stand-off is in the Indira Nagar locality, which touches the boundary wall of army headquarters and is regarded as one of a number of high-security zones in Srinagar.
It includes several paramilitary camps and the homes of two members of the state assembly.
The little-known separatist al-Mansoorein group has said two of its members launched the assault.
At least 40,000 people have died in Indian-administered Kashmir since the eruption of anti-Indian insurgency in the region in 1989. Separatists put the toll between 80,000 and 100,000.