The new violence followed the deaths of 23 people on Thursday that marked the bloodiest day since Pakistan and India agreed to resume talks a month ago on all issues including the disputed Himalayan territory.
Indian troops, backed by police and paramilitary forces, have stepped up operations against Muslim fighters.
Counter-insurgency police early on Friday shot and killed Muhammad Rafique, also known as Lidder, a senior commander of the hardline al-Umar Mujahidin guerrilla group that favours merging the Himalayan region with Pakistan.
Rafique "was killed in a counter-insurgency operation" in downtown Srinagar, the summer capital of Indian-administered Kashmir, a police spokesman said.
The group's supreme commander, Mushtaq Zargar, said Rafique had served as al-Umar's operational chief commander and called his death "a big loss to us".
"We will not allow his martyrdom to go waste," Zargar told local newspapers by telephone, naming Khalid Javed as the slain commander's successor.
In another clash in a wooded area in the village of Darwas Behak, near the northern town of Bandipora, six fighters and one soldier was killed, an army spokesman said.
Two fighters and three soldiers died in another clash in the southern Kashmir district of Poonch, police said.
"We will not allow his martyrdom to go waste"
supreme commander, al-Umar Mujahidin
Two other fighters were killed when security forces intercepted them as tried to sneak into Indian-administered territory across the Line of Control in Bimbergali in the south of Kashmir.
Officials say there have been at least half a dozen infiltration bids since the neighbours began a ceasefire last November along the line dividing the region.
Meanwhile, police said suspected fighters beheaded a Muslim man in the central Kashmiri district of Budgam on Friday, adding that the motive was unknown.
India and Pakistan are due to hold a first round of the talks between 16-18 February in Islamabad with Kashmir among subjects on the agenda.
India and Pakistan both claim Kashmir in full.