Suspected militants fired a rifle grenade at a prominent government building in the heart of India's Jammu and Kashmir state capital Srinagar on Saturday, officials said.
A constable of the Central Reserve Police Force (CRPF) was killed in the attack and a woman was injured, the police said.
The militants had aimed the grenade at the Civil Secretariat building which houses all important government departments including the office of the chief minister, CRPF spokesman P Tripathy said.
But the explosive landed near a cinema hall in the locality, he added.
The area around the Civil Secretariat building is a high-security area, but the militants escaped. There were not many people around as Saturday is a holiday, dpa reported.
Islamic militants have stepped up their activity in India-administered Kashmir in the past couple of weeks.
Suspected militants ambushed a group of Indian road workers on Friday in Kishtwar sector, about 265 kilometres north-east of the winter capital Jammu, killing five, including three soldiers of the Indian army who were providing protection for the group, the police said.
The group was ambushed by the militants in a manner similar to that used by the Taliban in Afghanistan, the Indian Express newspaper reported citing army sources.
Another dozen people were also injured in a grenade attack on Friday in Baramullah town, about 55 kilometres north of Srinagar. The militants were said to be targeting an army vehicle.
More than 60,000 people have died in the disputed Kashmir region since a violent secessionist militant movement began in the 1980s.
India, which has fought two wars with neighbouring Pakistan over Kashmir, claims the latter aids and abets Kashmiri militants. Pakistan denies the charge and calls Kashmiri militants freedom fighters.
Violence in Kashmir has lessened since India and Pakistan began a peace dialogue to resolve differences, including the Kashmir dispute, in 2004.