Thousands of people took to the streets in India again on Wednesday against a new citizenship law based on religion that has touched off violent unrest, and a southern state imposed curbs on public gatherings to pre-empt further demonstrations.

Prime Minister Narendra Modi's government says the Citizenship Amendment Act (CAA) is intended to address the persecution of non-Muslim minorities such as Hindus, Sikhs and Christians from Afghanistan, Bangladesh and Pakistan.

India's Supreme Court turned down a plea on Wednesday to halt implementation of the law but said it would hold hearings next month on the sweeping measure, which critics have described as anti-Muslim.

Protesters say the exclusion of Muslims betrays a deep-seated bias against the community, which makes up 14 percent of India's population, and that the law is the latest move in a series by the Hindu nationalist government to marginalise them.