Two army officers and one policeman were injured in the fighting in Chandigam, a village 45 kilometers (30 miles) south of Srinagar, the main city in the Indian portion of Kashmir, said a police officer who spoke on condition of anonymity because he was not authorized to talk to reporters.
A police statement said those killed were Kashmiri cadres of Lashkar-e-Taiba, a Pakistan-based rebel group that New Delhi accuses of staging a string of deadly attacks on India's financial capital of Mumbai in 2008. There was no independent account of the fighting and no rebel group has claimed involvement so far.
After the gunbattle, hundreds of villagers took to the streets chanting "We want freedom" and "Go India, go back," protesting government forces besieging them.
The police statement said officers shot and wounded seven civilians in the crowd after protesters threw rocks at police. Those injured were hospitalized but their conditions were not available.
The protest spread to neighboring Pulwama town, which was put under curfew.
Later Friday, the government ordered an inquiry into troops firing on the protesters with findings to be submitted within two weeks, said Shafat Noor, a state administrator.
The Himalayan region of Kashmir is divided between India and
Indian troops have largely suppressed an armed uprising launched in 1989, but public opposition to Indian rule still runs deep in Kashmir and is now mostly expressed in street protests where rock-throwing protesters and troops frequently face off.
More than 68,000 people have been killed in an armed rebellion against Indian rule and in an ensuing Indian crackdown.