Tension remained high at the epicentre of the unrest in Assam state's biggest city, Guwahati, with a fresh demonstration expected Sunday over the legislation even as some shops opened amid an easing of the curfew during the day.
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, three people died in hospital after being shot, while another died when a shop he was sleeping in was set on fire and a fifth after he was beaten up during a protest, officials said.
Two dead in India as police fire at demo against citizenship bill
Train services were also suspended in some parts of the east on Sunday after violence in eastern West Bengal state, with demonstrators torching trains and buses.
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.
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