Police detained hundreds of people in New Delhi and the southern city of Bengaluru today and shut down the internet in some places as protests entered a second week over a new citizenship law that critics say undermines India's secular constitution.

Citing law and order concerns following violent protests against the law during the past week, authorities imposed bans against public gatherings in parts of the capital and two big states - Uttar Pradesh in the north and Karnataka in the south.

Defying the bans, protesters held rallies at Delhi's historic Red Fort and a town hall in Bengaluru, Karnataka's state capital, but police swept in to round up people in the vanguard of those demonstrations as they tried to get underway.

In Bengaluru, Ramchandra Guha, a respected historian and intellectual, was taken away by police along with several other professors, according to an aide.

"I am protesting non-violently, but look they are stopping us," said Guha before being surrounded by police.

Police said they had detained around 200 people in the city, where according to protest organisers thousands of people attended four protests held in the city today.

At the Red Fort protest, academic-turned-politician Yogendra Yadav was among some 100 that police said they had detained.

"We are here to peacefully demonstrate against this law," Mohammed Maz, a bearded middle-aged protester told Reuters as he was led away by police.

Prime Minister Narendra Modi (above) has dug his heels in over the law that lays out a path for people from minority religions in neighbouring Muslim countries - Afghanistan, Bangladesh and Pakistan - who had settled in India before 2015 to obtain Indian citizenship.

Opponents of the law 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 ruling Bharatiya Janata Party to marginalise them.

Train stations around Red Fort were shut to prevent protesters joining the rally, and authorities also ordered mobile carriers to suspend internet services in some parts of the capital.

"As per the directive received from the government, data services are stopped at a few locations," Vodafone Idea's customer care tweeted in response to a user's question about its network in Delhi.

In Hyderabad, another major city in the south, 50 protesting students were detained by police, according to a media report said.

On Sunday, police stormed New Delhi's Jamia Millia University, firing tear gas and wielding batons to break up a protest by hundreds of students, injuring scores.

During a violent protest in another part of the capital this week, protesters, some masked, fought pitched battles with police.

Anger against Modi's government has burst into the open after a series of moves that were seen as advancing a Hindu-first agenda in a country that has long celebrated its diversity and secular constitution.

In August, the government took away Muslim majority Kashmir's autonomy and later the Supreme Court cleared the way for the construction of a Hindu temple on a site disputed by Muslims, and had been a flashpoint for years.

- Reuters