* Accenture, Wipro, Infosys shut Bengaluru offices
* Deadly riots over sharing of water between two states
* PM Modi calls for peaceful resolution of dispute
* Trade body estimates losses of up to $3.74 billion (Adds detail, link to video)
By Robin Paxton and Mamidipudi Soumithri
BENGALURU, Sept 13 (Reuters) - Indian and foreign technology companies including global outsourcing firm Accenture closed offices and told staff to stay home in the technology hub of Bengaluru on Tuesday after riots over the diversion of water from a river.
At least one person was killed in clashes between protesters and police that erupted after the Supreme Court ordered the southern state of Karnataka to divert some water from the Cauvery river to neighbouring Tamil Nadu state.
Businesses in Bengaluru, Karnataka's capital, have faced four days of disruption this month because of protests about the water dispute and an unrelated trade union-organised strike on Sept. 2.
This week's disturbances, in which dozens of vehicles were set on fire, have been the most serious in a city where gleaming new business parks are supposed to reflect the face of a modern, booming India.
Prime Minister Narendra Modi called on Karnataka and Tamil Nadu to resolve their differences peacefully.
"The violence and arson seen in the last two days is only causing loss to the poor, and to our nation's property," Modi said on Twitter.
The Cauvery river has been the source of tension between the two states for more than a century and violence over who gets access to water has flared before.
Karnataka's chief minister said that although the court ruling was difficult to abide by, his state would release water.
A Reuters witness said many shops were shuttered on Tuesday and fire trucks were stationed outside a major shopping mall, which was closed and had netting draped from its walls, apparently for protection.
Television footage showed largely deserted streets as riot police patrolled. Bengaluru airport said bus services to and from terminals were limited.
A curfew would be extended until Wednesday, police said.
Senior police officer L. Chandrashekar told Reuters police had arrested 355 people. He said one person had been killed when police opened fire on Monday to stop protesters torching vehicles with Tamil Nadu licence plates.
Media reported a second person had died after falling while fleeing a police charge, but this could not be confirmed.
BUSINESS PARKS AND TRAFFIC JAMS
Bengaluru, formerly known as Bangalore, is home to major Indian IT companies such as Infosys, Wipro and Mphasis , as well as startups like Ola and Flipkart.
Multinationals like Samsung Electronics, Oracle and Amazon.com also have offices in the city's business parks that have sprung up over the past decade or so.
Thousands of English-speaking Indians work in the city's call centres and back offices.
To many, Bengaluru symbolises India's rising economic vigour but the city has also been a victim of poor planning and congestion that can produce traffic jams for hours.
Indian software giants Infosys Ltd and Wipro were among the big employers to stay shut on Tuesday.
Thomson Reuters , which has offices with more than 4,500 staff in the city, said it was monitoring the situation closely and had activated "business continuity plans".
"The safety of our staff is our number one priority. As a result we do have a significant number of staff currently working remotely, alongside a small core group working from our offices: together ensuring it is business as usual for our clients," said head of corporate affairs and chief company spokesman David Crundwell.
Accounting giant E&Y on Monday advised its workers to leave early and avoid travelling in vehicles with Tamil Nadu plates in Karnataka, and vice versa for those in Tamil Nadu.
It advised employees to work from home on Tuesday, as did Amazon and Samsung in notes to their Bengaluru-based staff.
Amazon said the violence had affected delivery of some of its products in the city.
A source familiar with the situation said outsourcing giants had closed on Tuesday because not all staff could work from home. A spokesman for Wipro said Saturday would be a working day to make up for the day off declared on Tuesday.
Trade organisation ASSOCHAM said it estimated the violence had cost Bengaluru and the wider region up to 250 billion rupees ($3.74 billion) in losses, but it did not give a breakdown of how it came up with that figure.
"The image that India built around Bengaluru as its 'Silicon Valley' is being sullied," its secretary general, D. S. Rawat, said in a statement. ($1 = 66.8 rupees)
(Additional reporting Euan Rocha and Sankalp Phartiyal; Writing by Tommy Wilkes; Editing by Robert Birsel)