A policeman and a militant were killed in a gunbattle in Indian-controlled Kashmir on Monday, as shops and businesses remained closed in the disputed region to protest the killing of two people by the army.

Paramilitary spokesman Kishore Prasad said soldiers and police cordoned off a home in Mandoora village in southern Kashmir, acting on a report that suspected rebels were hiding there.

Prasad said the insurgents attacked troops with grenades and gunfire. Two soldiers were wounded in the clash.

In Kashmir's main city of Srinagar, schools were shut and shopkeepers closed their stores for a strike called by separatists to protest the killing of a man and a teenage boy by the army on Sunday in the northern village of Markondal.

The killings led to massive anti-India protests and clashes that spread to nearby towns and left five government troops injured Sunday.

Police have registered a murder case against the army. Army authorities have said they also will investigate the incident and expressed grief over the killings.

Rights groups say such investigations rarely lead to prosecutions and are mainly used to try to calm public anger.

On Monday, authorities ordered a curfew in the village and towns of Sumbal and Hajan to prevent protests.

However, hundreds of people defied the curfew and marched in Hajan and set fire to an army-run school while chanting slogans such as "We want freedom," a police officer said on customary condition of anonymity.

There were no students in the school because of the curfew and strike.

Clashes erupted in least at three places in the area as police and paramilitary soldiers fired tear gas and swung batons to stop rock-throwing protesters from marching to Markondal village, the officer said.

No injuries were immediately reported.

Syed Ali Geelani, a top separatist leader under house arrest, called for further protests on Friday.

"We reject this facade of investigation. Indian troops have license to kill anyone in Kashmir as they are protected by black laws," Geelani said in a statement Monday in which he demanded a probe by an international body.

Anti-India feelings run deep in Indian-held Kashmir, where about a dozen rebel groups have been fighting against Indian rule since 1989. About 68,000 people have been killed in the conflict.

The rebel groups have largely been suppressed by Indian troops in recent years, and resistance is now principally expressed through street protests.