The death toll from violent protests in northeast India against a contentious citizenship law has risen to six, officials said on Sunday, as authorities maintained internet bans and curfews to quell unrest.

Tensions remained high at the epicentre of the unrest in Assam state's biggest city, Guwahati, with troops patrolling the streets in vehicles amid tight security.

Some 5,000 people took part in a fresh demonstration in Guwahati on Sunday, with hundreds of police watching on as they sang, chanted and carried banners with the words “long live Assam”.

Officials said oil and gas production in the state was hit by the curfew, although the restrictions were eased during the day on Sunday with some shops opening.

The legislation, passed by the national parliament on Wednesday, allows New Delhi to grant citizenship to millions of illegal immigrants who entered India from three neighbouring countries on or before December 31, 2014 — but not if they are Muslim.

In Assam, four people died after being shot by police, while another was killed when a shop he was sleeping in was set on fire and a sixth after he was beaten up during a protest, officials said.

In West Bengal state, where protests stretched into a third day, Chief Minister Mamata Banerjee — who has spoken out against the national government's push for the law — suspended internet services in several districts.

Demonstrators set fire to tyres, staged sit-ins on highways and railway tracks, and torched trains and buses, with riot police brought in to disperse protesters and train services suspended in some parts of the east.

Home Minister Amit Shah on Sunday called again for calm, saying local cultures in northeastern states were not under threat, amid fears the new law will grant citizenship to large numbers of immigrants from neighbouring Bangladesh.

“Culture, language, social identity and political rights of our brothers and sisters from northeast will remain intact,” Shah told a rally in eastern Jharkhand state, News18 television network reported him as saying.

For Islamic groups, the opposition, rights activists and others in India, the new law is seen as part of Prime Minister Narendra Modi's Hindu-nationalist agenda to marginalise India's 200 million Muslims.

He denies the allegation.

Rights groups and a Muslim political party are challenging the law in the Supreme Court, arguing that it is against the constitution and India's secular traditions.

Modi's Bharatiya Janata Party (BJP) ally in Assam, which had supported the bill in parliament, told local media on Sunday that it now intended to challenge the law in the Supreme Court.