The protesters torched vehicles of the media and the police and pelted stones.
Unconfirmed reports said one of the deceased could have been hit by a bullet fired by the police.
Police spokesman Nisar Tamboli said only a postmortem would bring out what exactly caused the deaths.
Hundreds of people turned up at Azad Maidan Ground, the popular protest venue, in south Mumbai this afternoon on a call given by a city-based outfit, Raza Academy, to denounce the riots in Assam and also alleged attacks on minority community in Myanmar. Awami Vikas Party (AVP), a political outfit floated by former police officer Shamsher Khan Pathan, also took part in the protest.
The protesters suddenly turned unruly and set afire vehicles, damaged buses and indulged in stone-pelting.
Police opened fire and resorted to lathi-charge to disperse the mob, said a policeman deployed at the Azad Maidan.
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At least 55 persons were injured of whom two succumbed in a government hospital at south Mumbai.
"Two youths, Mohammed Umar (22) and Altaf Shaikh (18), who were injured in the violence and were in critical condition, died while undergoing treatment at St George Hospital," a civic body official told PTI.
Among the injured were some mediapersons, including Prashant Sawant of `Sakal Times' and Vivek Bendre of `The Hindu'. All injured were shifted to J J Hospital, St George Hospital, GT Hospital and Bombay Hospital, police said.
Maharashtra Chief Minister Prithviraj Chavan said in a statement that the Crime Branch has been asked to probe "whose hand was behind the violence and how the protest turned so violent".
He said altogether 45 police personnel and 10 others have been injured. (more)