Sabzar Ahmad Bhat, who reportedly succeeded Burhan Wani as the Hizbul Mujahideen commander, was killed on Saturday with another militant in an encounter with security forces in Tral area of Kashmir's Pulwama district.
The army's northern command said operations were on, suggesting a third militant was being engaged.
Six suspected militants were also killed in Kashmir's Rampur along the Line of Control on Saturday,
the army said.
Burhan Wani was killed on July 8 last year in south Kashmir. His killing sparked violent protests in the Kashmir Valley for months.
Joint Hurriyat leadership Syed Ali Geelani, Mirwaiz Umar Farooq and Muhamad Yaseen Malik calls for complete shutdown in the Valley on Sunday against the killing of Hizb Commander Sabzar Ahmad during an encounter in Tral.