Two civilians were also wounded.
Jain said Tanveer Ahmed Zargar, a district commander, and Imtiyaz Khan, his deputy, belonged to Hizbul Mujahedin, an Islamic armed group.
"They were involved in a number of bomb blasts and killings of civilians and security forces," Jain said.
Separately, police and soldiers shot dead Abu Haq, another Hizbul commander.
Police say he has been wanted for the last 15 years in connection with "a large number of killings".
More than 43,000 have been killed in Indian Kashmir since violence erupted in 1989.
Both India and Pakistan hold part of the Kashmir region but claim it in full.