Police opened fire on hundreds of protesters in southern India on Thursday, killing two, an official said, as fresh violence erupted around the country over a contentious citizenship law critics say is anti-Muslim.

And on the same day, a third fatality was also reportedly linked to protests in the northern state of Uttar Pradesh, where a man was hospitalized in Lucknow with a gunshot injury and died soon after.

The fatalities brought to nine the death toll from more than a week of unrest and came as authorities shut down internet and text messaging for tens of millions in India's most-populous state.

Deadly protests have broken out across India over a new law easing citizenship rules for people fleeing persecution from three neighboring countries - but not for Muslims.

Seven months after Modi swept to a second term, the law has stoked accusations at home and abroad that he wants to reshape India as a Hindu nation, which he denies.

The past week had already seen six people killed and dozens injured in the northeastern state of Assam.

On Thursday, authorities had banned gatherings across swathes of the country including all of Uttar Pradesh and Bangalore, areas of the northeast and parts of Bihar, New Delhi, Hyderabad and Chennai.

But that did not prevent tens of thousands from taking their anger onto the streets.

In Uttar Pradesh - home to some 200 million people - the government cut both mobile internet and SMS services after hundreds of protesters in the city of Samhbal set fire to vehicles and threw stones at security forces who responded with tear gas.

In New Delhi, metro stations were shut down, while authorities ordered telecom firms to cut calls, text messages and data in parts of the city.

Prominent rights activist Harsh Mander was detained in the capital, while in Bangalore the renowned historian Ramachandra Guha was among a number of protesters dragged onto a police bus.

In the northeast, where the protests originated last week, around 20,000 people marched in different locations - although this time no violence was reported.

The day's biggest demonstration took place in Malegaon district of Maharashtra state with as many as 60,000 people, police said.

(With input from AFP)