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 hardline 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.
