Police said the deaths occurred in two south Kashmir villages where hundreds took out demonstrations defying restrictions on the assembly of four or more people.
Security forces fired tear gas canisters, pellets and cane charged the protesters, several of whom were injured in Tukroo village of Shopian and Botengoo village of Anantnag, police said.
The deceased were identified as Sayar Ahmed Sheikh, 25, and Yawar Ahmed, 23.
Sheikh, according to police, was hit on the head by a flying tear gas shell. The Shopian man was removed to a hospital where he was declared brought dead, a police spokesperson said.
Ahmed, according to health officials, received pellet injuries in his chest and abdomen during a clash. He was also declared dead on the arrival at an Anantnag hospital.
With this, the death toll rose to 78 in the ongoing turmoil that has rocked the Kashmir Valley since the July 8 killing of Hizbul Mujahideen commander Burhan Wani.
Over 12,000 civilians and security personnel have been injured in the unrest that began a day after Wani's killing.
The valley has been observing a separatist-called shutdown for over two months.
The fresh violence came as hundreds of soldiers had started moving towards south Kashmir -- the worst hit region in the unending cycle of violence -- to help the civil administration re-establish authority in the valley.
The sources said the army had suspended its anti-militancy operations in the south for over two months because of the street unrest.
The fresh deployment of soldiers is to resume the counter-terrorism operations, the sources said. They said the army had been told not to get into mob control unless it came under attack by stone-throwing protesters.
Army Chief General Dalbir Singh is presently on a two-day visit to the Kashmir Valley. The sources said the chief's visit has been timed with the decision to move the army to the southern region.
On Saturday, curfew continued at many places in the valley to foil separatist-called protest rallies.
But people at various places, including in Srinagar, took out rallies, shouting anti-government and pro-freedom slogans.
