Supporting the militants, locals have been reported to have pelted stones on the forces as soon as the firing started.
Muneer Khan, Kashmiri police chief, said that fighting took place in the Shopian area. They were identified as Irfan, a tech-savvy militant involved in online propaganda for the militant outfit, and Umar, who was personal security man of Ghaznavi.
Khan said the three fighters belonged to the Hizbul Mujahideen group and were from nearby villages.
Heavy shelling and fires were exchanged between security forces and terrorists, who were tucked away in Awneera village of Shopian in South Kashmir.
In the morning on Sunday, police control room Shopian said that a house in which militants were hiding had been blown up. Two-three terrorists are suspected to trapped.
Trump again cites 'military' option against North Korea
During the call, both said they would boost efforts to enforce new sanctions and denuclearize the Korean Peninsula. US President Donald Trump said that Washington would respond with "fire and fury" to any possible threats.
One of the youth with bullet injury was identified as Sareer Ahmad Bhat of Shermal.
Another protester with pellet injuries to his eyes was referred by doctors to a hospital in Srinagar. Two Army jawans were also martyred in the encounter, while four others were injured.
Earlier, acting on specific information, the security forces surrounded Awneera village on Saturday evening upon which they were fired at by the militants, leading to the gunfight, a police spokesman said.
Meanwhile, authorities have directed telecom authorities to block mobile Internet services in Budgam district.
Three Kashmiri rebels and two Indian soldiers have been killed in a fierce gunbattle in the disputed Himalayan region, police said Sunday.