Protesters backed by the Vishwa Hindu Parishad (World Hindu Council) set fire to six churches and ransacked another four in the heart of Orissa state, police officer Narsingh Bol told AFP.
One young man was killed in the attacks and 30 more people hurt, according to local administrative official Satyabratu Sahu. Police would not specify the religion of the casualties.
The authorities imposed a curfew on four towns in Kandhamal district, where the violence broke out some 300 kilometres (190 miles) southwest of the state capital Bhubaneswar, he added.
The state's chief minister appealed for peace.
"Orissa is known for its long tradition of communal amity. Let's maintain it," said Naveen Patnaik in a televised speech.
Some 500 policemen were deployed to restore peace, state police chief Gopal Nanda said, and more were on the way.
Gouri Prasad Rath, a state leader of the Hindu council, told AFP that Hindu temples had been attacked as well but police could not confirm the claim.
Authorities say the church violence came after a Hindu leader called Swami Laxmananand Saraswati, who has campaigned against what he calls the "forced" conversion of low-caste Hindus to Christianity, was attacked on Christmas eve.
India's Catholic leadership meanwhile said the church was shocked and urged New Delhi to provide security for the community.
The "well-planned attacks on innocent Christians and their leaders have completely shocked us," the Catholic Bishops Conference of India said in a statement.
"We are deeply pained at a time when we are celebrating peace and harmony of Christmas. It is most important that the tiny minority community of Orissa feels safe and secure to carry on with their normal life and activities."
Christian missionaries have long found willing converts among India's neglected tribal communities or "untouchable" Hindus -- known as Dalits -- who still face massive discrimination.
In Kandhamal, the majority of Christian converts are Dalits.
Orissa's four-decade old "Freedom of Religion Act" requires every change of religion to be cleared by the authorities. Hindus say the missionaries fail to do so.
A Hindu man is serving a life sentence for burning alive an Australian Christian missionary and his two sons as well as a Catholic priest in Orissa in 1999.
Graham Staine, who had worked for three decades with lepers, and sons aged eight and 10 died when a Hindu mob torched a jeep in which they were sleeping.
Sectarian clashes break out periodically in the billion-plus country of multiple faiths, where approximately 2.3 percent are practising Christians.
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