Police fired shots in the air as thousands of protesters took to the streets on Tuesday in the latest clashes in the Indian capital over a new law that makes it easier for non-Muslims from three neighboring countries to gain citizenship.

Nationwide opposition to the Citizenship Amendment Bill (CAB) — which offers a path to Indian citizenship for religious minorities from Afghanistan, Bangladesh and Pakistan — has grown since last week, but Prime Minister Narendra Modi's government appears to have dug in its heels.

The Indian prime minister was adamant that the CAB, passed last week, would not affect Indian nationals, including Muslims. "It's as clear as being engraved in stone that the CAB will not affect any citizen — Muslim, Hindu, Christian or anyone else," said Modi told a political rally in eastern Jharkhand state.

"Both my government and I are firm like a rock that we will not budge or go back on the citizenship protests," said Home Minister Amit Shah.

But critics say the law weakens India's secular foundations since it does not apply to Muslims, who have been coming out on to the streets in increasing numbers against the legislation.

Tens of thousands more rallied in West Bengal, Kolkata and Tamil Nadu states on a sixth day of nationwide protests.

In the eastern city of Kolkata, more than 20,000 protesters joined a fresh march led by West Bengal Chief Minister Mamata Banerjee, a fierce critic of Modi.

Banerjee, who also led protests on Monday, said the law would not be implemented "for as long as I am alive".

Train services were disrupted after railway tracks were blocked by protesters, while nearly 700 people have been arrested, Banerjee said.

Authorities have imposed internet blackouts and used force to shut down rallies and sit-ins across several states.

The new round of rallies came as the Supreme Court on Tuesday referred petitions calling for a probe into allegations of police brutality to the states' High Courts.

Rioters had torched vehicles while police with batons fired tear gas and charged protesting students before storming Delhi's Jamia Millia Islamia university late Sunday.

(With input from AFP)