Two more people have died in protests over India's controversial new citizenship law bringing the death toll to eight, as police detained hundreds of people and cut internet services while crowds defied bans on public gatherings.

At least one of those killed in the southern city of Mangaluru, had been shot, hospital officials told Reuters amid clashes between stone-throwing crowds.

Authorities erected roadblocks and for the first time blocked internet access in the capital, Delhi, as they tried to quell nationwide anger.

Protests have now raged for a fortnight over Narendra Modi's new legislation, which opponents say undermines India's secular foundation and represents a drive to bring India closer to a Hindu state. Thursday's deaths are thought to bring the total to eight.

Mobile phone companies said they had been ordered to cut internet services in parts of the capital.

While India regularly shuts down internet as a public order measure, the Software Freedom Law Centre, a digital freedom watchdog, said it was the first time it had been cut in Delhi.