Protesters in New Delhi shouted slogans against Indian Prime Minister Narendra Modi's government on Saturday, saying Muslims were violently targeted by authorities in the aftermath of Hindu-Muslim clashes.

The clashes on Sunday during a religious festival prompted police to impose a curfew in one town and ban gatherings of more than four people in parts of three states ruled by Modi's Hindu nationalist party.

Local authorities tore down the homes and shops of suspected Muslim rioters in central Madhya Pradesh state in the aftermath of the violence that broke out during the Hindu festival of Ram Navami, according to a police official who did not want to be named.

In Modi's home state, Gujarat, authorities demolished makeshift shops belonging to those they said were involved in the riots in which one man was killed, said an official in Anand district in Gujarat, where the clashes erupted.

Police and local authorities told Reuters after the clashes that they were free from bias and acting within the law.

Opposition politicians have accused Modi's right-wing Hindu nationalist Bharatiya Janata Party of stoking tensions between majority Hindus and Muslims in states that it rules.

Police in India's most populous state of Uttar Pradesh on Friday arrested nine people from a hard-line Hindu group suspected of torching the home of a Muslim man who married a Hindu woman. At the protest attended by scores of people in New Delhi, Kavita Krishnan, a social activist, said India was being transformed from a constitutional democracy to a Hindu supremacist state.

Leaders of 13 opposition parties made a joint statement calling for peace and harmony and after the religious clashes.

"We are extremely anguished at the manner in which issues related to food, dress, faith, festivals and language are being deliberately used by sections of the ruling establishment to polarize our society," the leaders said.