Protesters angered by India's new citizenship law that excludes Muslims have defied a ban against demonstrations, as Prime Minister Narendra Modi defended the legislation.

Twenty-three people have been killed nationwide since the law was passed in parliament earlier this month in protests that represent the first major roadblock for Modi's Hindu nationalist agenda since his party's landslide re-election last spring.

Most of the deaths have occurred in the northern state of Uttar Pradesh, where 20 per cent of the state's 200 million people are Muslim.

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Police, who deny any wrongdoing, said among the 15 people killed in the state was an eight-year-old boy who died in a stampede in the city of Varanasi, the heart of Modi's parliamentary constituency.

Since last week, police in Uttar Pradesh have taken nearly 900 people into custody for engaging in violence.

Authorities across the country have scrambled to contain the situation, banning public gatherings under Section 144, a British colonial-era law, and blocking internet access.

India's ministry of information and broadcasting issued an advisory on Friday night asking broadcasters across the country to refrain from using content that could inflame further violence.

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A group of politicians from the opposition Trinamool Congress party who travelled to Uttar Pradesh on Sunday to meet with families of those killed in the violence were not permitted to leave the airport runway, police said.

"We will not permit them because Section 144 is imposed in the area and it can make the atmosphere more tense," said Uttar Pradesh's police chief, OP Singh.

In the southern state of Tamil Nadu, about 500 Muslim and leftist activists protested, defying a ban on public gatherings there.

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Meanwhile, Modi took the stage at a rally in the capital launching his Bharatiya Janata Party's campaign for New Delhi legislative assembly elections in February, and quickly turned to the contentious new law.

"People who are trying to spread lies and fear, look at my work. If you see any trace of divisiveness in my work, show it to the world," he said.

Modi accused the main opposition Congress party of conspiring to "push not only New Delhi but other parts of the country into a fear psychosis".

READ MORE India protests rage against citizenship law, but Narendra Modi remains defiant

"They are trying every tactic to push me out of power," he said, urging protesters to desist from attacks on police and other violence.

The new law allows Hindus, Christians and other religious minorities who are in India illegally to become citizens if they can show they were persecuted because of their religion in Muslim-majority Bangladesh, Pakistan and Afghanistan. It does not apply to Muslims.

Critics have slammed the legislation as a violation of India's secular constitution and have called it the latest effort by Modi's government to marginalise the country's 200 million Muslims.