Medics rush the injured child to the emergency ward of a hospital in Srinagar.

New Delhi has bolstered counter-insurgency efforts in the restive territory, with at least 33 separatist militants killed this month.

The child was in a car that drove into a gun battle between suspected rebels and paramilitaries near the town of Bijbehara, a police officer told reporters.

Residents gathered around the body of the child in Srinagar.

"The boy and a soldier were injured during the exchange of fire and both later died in hospital," said the officer, who asked not to be named.

Three rebels were killed in a separate firefight at Chewa, near the region's main city Srinagar, in a battle that lasted 20 hours, army spokesman Colonel Rajesh Kalia said.

Armed clashes are frequent in Indian Kashmir but have increased in recent weeks.

Indian soldiers and a policeman open fire during an encounter in Srinagar. File/ AFP

An insurgency launched three decades ago has claimed tens of thousands of lives.

India has 500,000 soldiers stationed in Kashmir.

Tensions have mounted again in Kashmir since August last year when India revoked the region's semi-autonomous status, detained local political leaders and imposed a months-long internet and mobile phone blackout.