The incident prompted police to launch a probe and a case of attempt to murder has been registered in this regard.
"We have begun our probe after we registered a case under section 307 (attempt to murder) of IPC and under relevant sections of the Arms Act against six unknown persons," said Kiran Kumar Chavan, DCP, Port Zone.
On the line of probe, another official said they will investigate on the circumstances under which shots were fired and will write to Navy and ONGC to join the probe if need be.
The incident occurred yesterday when the ISV was providing protection to the offshore oil rig.
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"While providing protection to the offshore oil rig, ISV yesterday noticed a fishing boat anchored close to an oil platform. Despite repeated warning when the boat refused to move out of the prohibited area, warning shots were fired into the water," Navy stated in an official release.
The bullet accidentally hit a fisherman on the boat, it said.
The fisherman was immediately evacuated by helicopter to a hospital ashore for treatment. His condition is currently stable.
The incident was immediately reported to the Joint Operations Centre which is manned round the clock and where all authorities concerned with coastal security are present. The fisherman's relatives have also been informed, they said.
The fishing boat came close to one of the oil platforms of the Oil and Natural Gas Corporation Ltd (ONGC) located in Bombay High whose oil rigs are secured by the Navy.
Meanwhile, an ONGC official, denying any role in the firing incident as alleged by a section of fishermen, said in fact the corporation, after spotting the fisherman wounded, brought him to one of the platforms in their western offshore field and gave him first aid.