Thousands of Indians are set to ring in the New Year by holding protests against a citizenship law, despite Prime Minister Narendra Modi's attempts to dampen demonstrations that have run for nearly three weeks.

India has been rocked by the protests since December 12, when the government passed legislation easing the way for non-Muslim minorities from the neighbouring Muslim-majority nations of Afghanistan, Bangladesh and Pakistan to gain Indian citizenship.

Combined with opposition to a proposed national register of citizens, many Indians fear the move will discriminate against the minority Muslim community and chip away at the country's secular constitution.

Protesters plan at least three demonstrations in New Delhi, the capital, including the area of Shaheen Bagh, where hundreds of residents have blocked a major highway for 18 days.

Poetry recitals and speeches are planned by organisers at a protest outside New Delhi's Jamia Millia University, which was stormed by police this month.

“New Year's resolution to defend the constitution,” read the schedule for another protest planned in New Delhi, now in the grip of its second coldest winter in more than a century.

Police said they planned to deploy additional forces in New Delhi on New Year's Eve, with traffic curbs imposed in some parts of the capital.

“All precautionary measures are in place,” said police official Chinmoy Biswal, who oversees the southeastern part of the city that includes Shaheen Bagh and Jamia Millia University.

“Recently, there have been no incidents. So we hope things will remain fine,” he told Reuters.

In the southern city of Hyderabad, at least two small groups of demonstrators have been organising flash protests, to skirt police restrictions on larger gatherings.

Typically, half a dozen demonstrators pop up in public places, such as malls and coffee shops, holding up placards and encouraging passersby to join in, a member of one of the groups, which has held 11 protests, told Reuters.

“Every day, we are doing something, somewhere,” said the person, who sought anonymity for reasons of security, adding that another protest is planned to be staged on Tuesday night.

Street-side poetry recitals, stand-up comedy, and music performances are also planned in the financial capital of Mumbai and the eastern city of Kolkata.

All three cities have seen large, peaceful protests against the Citizenship Amendment Act (CAA) and the National Citizens' Register (NRC), which were part of the election manifesto of Modi's ruling Hindu nationalist party.

But some protests have turned violent, particularly in the populous northern state of Uttar Pradesh, and at least 25 people have been killed in clashes with police since early December.

Initially caught off guard by the scale of the protests, Modi's Bharatiya Janata Party (BJP) has scrambled to douse public anger, with Modi declaring that there had been no discussions on the NRC, contradicting party colleagues.

The BJP has also launched an effort, backed by a social media campaign, to explain that the CAA is not discriminatory and is needed to help non-Muslim minorities persecuted in the three neighbouring countries.