Police detained more than 100 protesters in key Indian cities on Thursday as they defied a ban on protests that authorities hope to stop widespread demonstrations against a new citizenship law that opponents say threatens the secular nature of Indian democracy.

Dozens of demonstrations were to take place around the country as opposition grows to a new citizenship law that excludes Muslims. The law has sparked anger at what many see as the government's push to bring India closer to a Hindu state.

Historian Ramchandra Guha, a biographer of India's independence leader Mohandas Gandhi, was among those detained in Bangalore, the capital of southern Karnataka state.

When reached by the phone, Guha said he was in a bus with other detainees and did not know where the police were taking them.

In New Delhi, Yogendra Yadav, the chief of the Swaraj India party, was among those detained as protesters said they would go ahead with a demonstration at New Delhi's iconic Red Fort and surrounding historic district.

Internet service was blocked in some parts of New Delhi, a tactic Indian authorities are known to use in other parts of the country, such as occupied Kashmir, to try to stop protests from being organised. Such tactics are rare for the capital.

The new citizenship law applies to Hindus, Christians and other religious minorities who are in India illegally but can demonstrate religious persecution in Muslim-majority Bangladesh, Pakistan and Afghanistan. It does not apply to Muslims.

Critics say it's the latest effort by Prime Minister Narendra Modi's Hindu nationalist-led government to marginalise India's 200 million Muslims and a violation of the country's secular constitution.

Modi has defended it as a humanitarian gesture.

The law's enactment last week follows a contentious process in northeastern Assam state intended to weed out people who entered illegally. Nearly two million people in Assam were excluded from an official list of citizens, about half Hindu and half Muslim, and have been asked to prove their citizenship or else be considered foreign.

India is also building a detention centre for some of the tens of thousands of people the courts are expected to ultimately determine have entered illegally. Modi's interior minister, Amit Shah, has pledged to roll out the exercise nationwide.

Some Indian Muslims fear it's a means by which Hindu nationalists can put them in detention or deport them from the country.

On Wednesday, authorities tightened restrictions on protesters, expanding a blockade of the internet and a curfew in Assam.