More than 100 Hindu families have fled Kashmir as panic spread after the killing of a Hindu school teacher in India's only Muslim-majority region, a community leader said on Wednesday.

Militants on Tuesday shot dead Rajni Bala, 36, outside a government school in Kulgam that lies south of Kashmir's main city of Srinagar - the latest in a spate of targeted killings of Hindus and Muslims.

India has been fighting an armed insurgency in Kashmir since the late 1980s.

Avtar Krishan Bhat, president of a Hindu Kashmiri Pandit colony in northern Kashmir's Baramulla, said that around half of the 300 families living in the area had fled since Tuesday.

"They were terrified after yesterday's killing. We will also leave by tomorrow as we are waiting for a government response," he said. "We had asked the government to relocate us outside Kashmir."

Residents said police had sealed off a Hindu area in Srinagar and stepped up security around places where Kashmiri Pandit government employees live.

The local administration did not immediately respond to a request for comment on families fleeing, but the region's top government official, Lieutenant Governor Manoj Sinha, last month assured Kashmiri Pandits that measures would be taken for their security.

India and its arch rival Pakistan both claim Jammu and Kashmir - which New Delhi reorganised into two federally administered territories in 2019 - in full but each only controls one part of the Himalayan region.

Some 250,000 Kashmiri Pandits left the Kashmir valley because of a sharp rise in killings of Hindus and attacks on their homes at the start of a rebellion by Muslim militants in 1989.

Last month, a Kashmiri Pandit working for the local government was shot dead inside his office, leading to protests by other employees from the minority community who demanded re-location to safer areas outside the Kashmir valley.

"We have killed all those militants who were responsible for the earlier killings," Kashmir valley's police chief Vijay Kumar told Reuters on Wednesday.