Fresh protests rocked India on Monday as anger grew over new citizenship legislation slammed as anti-Muslim, after six people died in the northeast and up to 200 were injured in New Delhi.

The law fast-tracks citizenship for non-Muslims from three neighbouring countries. Critics say it is part of Prime Minister Narendra Modi's Hindu nationalist agenda to marginalise the 200-million strong Islamic minority.

Modi on Monday denied this, tweeting that the new law "does not affect any citizen of India of any religion", while accusing "vested interest groups" of stoking the "deeply distressing" unrest.

Rahul Gandhi, former opposition Congress chief, tweeted that the law and a mooted nationwide register of citizens also seen as anti-Muslim were "weapons of mass polarisation unleashed by fascists".

The UN human rights office said last week it was concerned the law "would appear to undermine the commitment to equality before the law enshrined in India's constitution", while Washington and the European Union have also expressed unease.

On Monday fresh protests took place including in Chennai, Bangalore and Lucknow, where hundreds of students -- most of them Muslims, television pictures indicated -- tried to storm a police station.

The northeast, where even allowing non-Muslims citizenship is opposed by many locals and which in recent days has been the epicentre of protests with six people dead, also saw fresh demonstrations.

Authorities there in Assam's main city Guwahati lifted a daytime curfew but night-time restrictions remained, as did internet curbs. Ten people remain in hospital with gunshot wounds, while 190 people have been detained.

"The curfew is from 9:00 pm to 6:00 am," Assam finance minister Himanta Biswa Sarma said.

In the east in Kolkata, capital of West Bengal, more than 10,000 people took part on Monday in a march led by state premier Mamata Banerjee, a firebrand Modi opponent.

Banerjee told the crowd that the law would be implemented in her state "over my dead body," Indian media reported.

"India is being divided," said Meera Hajra, a protester in Kolkata.

State police said they fired tear gas to disperse hundreds of protesters elsewhere after they threw stones. More than 350 people were detained.

- Buses torched -
No major incidents were reported nationwide by Monday evening, although several metro stations were closed in Delhi as demonstrations there continued for a second day.

On Sunday evening rioters torched vehicles and police with batons fired tear gas and charged protesting students before storming the Delhi's Jamia Millia Islamia university.

The university's vice-chancellor Najma Akhtar said on Monday that 200 people were injured but police put the number at 39 students hurt with 30 officers also injured, one of them critically.

Police spokesman MS Randhawa said that four buses, 100 private vehicles and 10 police bikes were damaged, and that officers exercised "maximum restraint, minimum force" despite being "provoked".

He denied some media reports that police opened fire. News channel NDTV reported that two people were in hospital with bullet injuries.

The clashes prompted university students to demonstrate elsewhere including in the southern state of Tamil Nadu and in Bangalore.

"I want to make it clear, nobody is scared. Like people in Hong Kong are protesting, in Chile they are protesting, and they are not scared," student Bhumika Saraswati told AFP in the capital.

Fellow student Shree Kumar said that the citizenship law was "against the Muslims. It's against the ethos of India. It's against the secular ideas of India."

Authorities in Uttar Pradesh state cut internet access in some parts following clashes between demonstrators and police in Aligarh on Sunday that saw 21 people arrested, authorities said.

Modi has said Muslims from Pakistan, Bangladesh and Afghanistan are not covered by the law because they have no need of India's protection.

Ashok Swain, a professor at Sweden's Uppsala University said that the scale of the protests had caught Modi's government off guard.

"This certainly will add pressure on the regime when the economy has failed," Swain told AFP.