At least 25 people have died in almost two weeks of demonstrations and violence after the government passed the contentious law earlier this month, with most deaths reported from the northern Uttar Pradesh state, home to nearly 204 million people, 20 percent of whom are Muslims.
Modi's Bharatiya Janata Party (BJP) governs Uttar Pradesh, whose Chief Minister Yogi Adityanath, a controversial Hindu monk, had promised "revenge" against people protesting the new law.
So far, 17 people have been killed and thousands arrested in two weeks of protests in Uttar Pradesh, while unverified videos of police attacking protesters, including children, with batons and raiding homes have been shared widely on social media.
The new law, the Citizenship Amendment Act (CAA), allows Hindus, Christians and other religious minorities who are in India as undocumented migrants to become citizens if they can show they were persecuted because of their religion in Muslim-majority Bangladesh, Pakistan or Afghanistan.
The CAA does not apply to Muslims, leading to criticism of it violating India's secular constitution and aimed at marginalising 200 million Muslims, who constitute nearly 14 percent of the country's 1.3 billion people.
Nearly two million people, about half of them Muslim, were excluded from an official list of citizens - called the National Register of Citizens (NRC) - and have been asked to prove their citizenship or else be considered foreign.
Addressing an election rally in the capital, New Delhi, Modi on Sunday said: "Muslims who are sons of the soil and whose ancestors are the children of mother India need not to worry."
However, he contradicted Minister of Home Affairs Amit Shah, saying there had been no discussion yet of whether to execute a nationwide NRC.
In several public statements, Shah has pledged to roll out the process nationwide.
Modi also denied the existence of a detention centre, accusing the Congress party of spreading fear that Indian Muslims would be jailed there.
He said his opponents were "spreading rumours that all Muslims will be sent to detention camps". "There are no detention centres. All these stories about detention centres are lies, lies and lies," he said.
Assam has six detention centres holding more than 1,000 alleged "illegal" migrants, and plans another 11. India's junior home minister has told Parliament that 28 detainees have died in the camps in recent years.
Shah's ministry in June issued a "2019 Model Detention Manual" to states, asking them to set up camps in major entry points. Two centres were planned near the cities of Mumbai and Bengaluru.
Nationwide protests rage on
The protests against the law began in Assam, the centre of a decades-old movement against migrants, before spreading to predominantly Muslim universities and then nationwide.
On Monday, the Congress party held a silent protest in the capital against the new law, a day after Modi accused the opposition of pushing the country into a "fear psychosis" over the legislation.
The party's former president, Rahul Gandhi, urged young people in New Delhi to join the protest at Raj Ghat, a memorial dedicated to Mahatma Gandhi.
The Congress and other groups in New Delhi have filed nearly 60 petitions challenging the constitutional validity of the law in the Supreme Court, which has asked the federal government to respond to the pleas by mid-February.
In the southern city of Chennai, more than 100,000 people joined what the police described as a peaceful march against the law, a spokesman for the DMK regional party said.
Similar protests were also held in other southern cities, including Bengaluru and Kochi.
Modi's 'single-most divisive' move
The backlash over the citizenship law represents the first major roadblock for Modi's Hindu nationalist agenda since his party's landslide re-election earlier this year.
Authorities have so far taken a hard-line approach to quell the protests, evoking a British colonial-era law banning public gatherings.
Internet access has been periodically blocked in some states, and the Ministry of Information and Broadcasting has asked broadcasters across the country to refrain from using content that could inflame further violence.
Protests against the law also came amid a continuing crackdown in Muslim-majority Indian-administered Kashmir, the restive Himalayan region stripped of its semi-autonomous status and demoted from a state into a federal territory in August.
Darul Ihsan Media Desk