(Recasts with fresh protests) SRINAGAR, India, Feb 6 (Reuters) - Police fired teargas on Tuesday to disperse hundreds of people in Indian Kashmir protesting the alleged killings of civilians in staged gun battles with security forces, police and witnesses said. At least five policemen were injured in clashes with stone-throwing protesters in downtown Srinagar, Kashmir's summer capital. A strike called by a political separatist group, Jammu Kashmir Liberation Front (JKLF), closed much of the Kashmir Valley, witnesses said. Over the weekend, authorities arrested four policemen, including two senior officers, accused of killing three people in the Ganderbal area outside Srinagar late last year and passing them off as militants fighting New Delhi's rule in the region. "(The) Peace process and killing of innocent Kashmiris cannot go together," JKLF chairman Mohammad Yasin Malik said. On Monday, officials said both the army and police had begun investigations into the deaths of the three men. Most anti-insurgency operations are jointly conducted by army troops, local and federal police. Malik, along with dozens of activists, began a three-day fast near the front's office in the heart of Srinagar. Earlier on Tuesday, hundreds of people, led by veiled women, marched through deserted streets of Srinagar as the strike closed shops and businesses. "We want freedom ... down with security forces," the protesters shouted. India and Pakistan claim the disputed Kashmir region in full but rule it in parts. They began the latest peace moves in 2004. "Nobody, of whatsoever position or rank he may be, would be spared if found guilty of innocent killings and deliberate human rights violations," Jammu and Kashmir Chief Minister Ghulam Nabi Azad said. Police say they have so far exhumed five bodies as part of their investigation into the Ganderbal killings. New York-based Human Rights Watch groups has called for an end to "fake encounters" in Kashmir. "This epidemic of fake 'encounter killings' by the security forces has plagued Kashmir for too long," Brad Adams, the group's Asia director, said last week. Local officials and analysts say the police and soldiers enact fake gun battles by killing civilians to get cash awards and promotions that are given for killing Muslim militants. More than 40,000 people have been killed in a revolt against Indian rule in the Himalayan region since 1989, officials say. Human rights groups put the toll at about 60,000 dead or missing.