The policeman was killed and four people, including two civilians, were wounded on Tuesday when suspected separatist fighters lobbed a grenade at a police patrol vehicle in a crowded market in the heart of Srinagar, Kashmir's summer capital.
A spokesman for the Pakistan-based Jaish-e-Mohammad group claimed responsibility for the attack in calls to local newspapers.
In other incidents, at least 13 labourers were wounded when suspected fighters hurled a grenade at a security vehicle near a bus stop in Sopore town, 45km from Srinagar, where four pedestrians were also hurt in another grenade attack.
The attacks coincided with talks between Indian and Pakistani officials in the Pakistani capital, Islamabad, on terrorism and the trafficking of drugs and people.
Separatists fighting Indian rule in Kashmir, divided between the South Asian nuclear rivals but claimed in full by both, have stepped up their attacks in recent weeks.
More than 45,000 people have been killed since a revolt broke out in 1989 in Jammu and Kashmir, mainly Hindu India's only Muslim-majority state.