Indian Prime Minister Narendra Modi's move to drive the law through parliament last week has ignited nationwide protests that have often turned violent, with six people killed.
The law gives migrants fleeing persecution from neighbouring Afghanistan, Pakistan and Bangladesh an easier path to citizenship, except that Muslims are excluded.
Critics say it is further proof that Modi, emboldened by a resounding election victory this year, is moving quickly to reshape India as a Hindu nation and weaken its secular foundations.
Pakistani Hindus reject India’s offer for citizenship
During the past week of unrest, hundreds of people have been arrested, authorities have cut the internet in some flashpoint areas and banned large gatherings in others.
Police have fired tear gas into crowds and been accused of beating protesters, including women and students, fuelling the anger.
Protest organisers have flagged plans for major rallies on Thursday in major cities across India, including the capital of New Delhi.
Police refused a march permit for one of two major demonstrations planned in New Delhi, officials said. Organisers said they planned to march anyway.
Authorities on Wednesday also imposed a ban on gatherings of more than four people in some of the city's Muslim-dominated districts.
A crowd of mostly young people rallied outside Delhi's Jamia Millia Islamia University on Wednesday to protest, defying the ban on large gatherings.
"We are really very angry with the BJP government... they have taken racism to the extreme point," Taiba Hadis, 18, told AFP at the rally.
"They are questioning our existence, and it is high time for us to speak up."
In the financial capital of Mumbai, hundreds of people rallied on Wednesday carrying placards with the words: "India is Ours" and chanting "We Are All One".
"We just cannot go along with this bill. I can't believe we now have to prove our citizenship after living in India for so many years," Tabeer Rizvi told AFP as the Mumbai crowd burst into a Hindi version of the
India citizenship law protests spread across campuses
US civil rights movement anthem: "We shall overcome".
"I am not surprised to see people of all religions come out to protest this bill."
Rallies were also held in other states including West Bengal, Tamil Nadu and Telangana on Wednesday.
The UN secretary-general's spokesperson Stephane Dujarric said Tuesday the global body was "concerned about the violence and alleged use of excessive force by security forces that we've seen that have been taking place".
The US State Department this week urged New Delhi to "protect the rights of its religious minorities in keeping with India's constitution and democratic values"
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