State director-general of police Ashok Prasad said the situation was tense, although no fresh violence was reported Saturday.
Troops in armored vehicles drove through the streets of Kishtwar, a town 125 miles (200 kilometers) southeast of Srinagar, the main city in Indian-controlled Kashmir, where rival groups attacked each other on Friday with firearms, stones and sticks.
Scores of shops, two hotels and one gas station were set on fire by the mobs, police said.
The trouble erupted Friday after Hindus objected to Muslims shouting pro-independence slogans on the Eid Al-Fitr holiday, which caps the fasting month of Ramadan.
Anti-India feelings run deep in Kashmir, where about a dozen rebel groups have been fighting against Indian rule since 1989. More than 68,000 people, mostly civilians, have been killed.
The rebel groups have largely been suppressed by Indian troops in recent years, and resistance is now principally expressed through street protests.
One Muslim was burned to death and one Hindu died of gunshot wounds in Friday’s clashes, a police officer said on condition of anonymity as he was not authorized to talk to reporters. He said 24 people were being treated in hospitals, but their injuries were not life threatening.
“The curfew is being strictly enforced. We are not taking any chances as the situation has the potential to have serious ramifications for the entire state,” Prasad said.
He said police were working to identify the troublemakers.
Indian authorities ordered an inquiry into the rioting and replaced the local police chief and the top civil administrator as part their efforts to restore peace in the town.
Authorities asked all members of the Village Defense Committee in the area to hand their weapons over to the police. The government provided weapons to a more than 20,000-strong semiofficial force created in the early 1990s to counter insurgency in the region. The members are mostly drawn from Hindu community.
Kashmir is divided between India and Pakistan. They have fought two wars over its control since they won independence from Britain in 1947.
The Indian portion of Kashmir is the only Muslim majority state in a predominantly Hindu country.