Prime Minister Narendra Modi appealed for calm Tuesday in the Indian tech hub of Bangalore which was placed under curfew after deadly violence erupted over a water dispute with a neighbouring state.

Thousands of police officers were deployed on the largely deserted streets of the southern city to enforce the curfew, after rampaging, stone-pelting mobs set buses and cars ablaze on Monday.

One protester was killed on Monday after police fired on a mob trying to torch a police car, a senior officer said. A man also died Tuesday of injuries he suffered while trying to escape baton-wielding police the day before, officials said.

Modi called the violence "distressful" and urged restraint in the city known as India's Silicon Valley, home to local IT companies as well as offices of international giants such as Amazon and Microsoft.

"This dispute can only be solved within the legal ambit. Breaking the law is not a viable alternative," Modi said in a series of tweets.

"The violence and arson seen in the last two days is only causing loss to the poor, and to our nation's property."

Protests erupted after the Supreme Court ordered Karnataka state, of which Bangalore is the capital, to release water from a river to ease a shortage in Tamil Nadu until later this month.

India suffers severe water shortages that cause frequent tensions between states and the row over sharing the Cauvery River which starts in drought-hit Karnataka stretches back decades.

Karnataka chief minister Siddaramaiah vowed to protect the thousands of Tamils living in the state after mobs targeted dozens of vehicles with Tamil licence plates.

- 'Grave injustice' -

A curfew was imposed in 15 areas of the city "to maintain peace and prevent untoward incidents" during the Muslim holiday of Eid, Bangalore police commissioner N.S Megharikh told reporters.

More than 300 protesters have been arrested over the violence, which has forced shops and offices to close, state home minister G. Parameshwar said.

Both Amazon India and local rival Flipkart, which are based in Bangalore, said their services have been disrupted, while some companies told staff to work from home.

"We will resume all deliveries at the earliest," an Amazon spokesperson told AFP.

While Bangalore was calm on Tuesday, protests were held along the 150-kilometre (93-mile) highway from the state capital to Mysore city.

"A grave injustice is being done to us as the state is forced to release more water for growing crops in Tamil Nadu when we don't have sufficient water for even drinking because of deficit rains," protest organiser Pravish Shetty told local TV.

Bus services between the two states have also been suspended, with a Tamil Nadu service owner saying 30 of his vehicles had been torched outside Bangalore.

"A group of unidentified miscreants barged into our bus yard and set 30 of our coaches on fire with kerosene or petrol," Rajesh Natarajan, managing director of KPN Tours & Travels, told local television.

Earlier this year the government was forced to deploy troops to secure a canal supplying water to New Delhi after it was sabotaged by protesters in neighbouring Haryana state, causing days of shortages in the capital.