The 10 minutes of footage on YouTube shows three vessels, one a Taiwanese longline tuna fishing boat with identification number BI-2353, manoeuvring around a smaller vessel.
The video then shows men in the water clinging to debris being repeatedly shot and bleeding heavily in the water.
One man struggles to stay afloat for several minutes while bleeding profusely before being shot again and ends up floating motionless.
Close-ups of the bodies floating face down in the water are followed by the boat crew taking selfies with their mobile phones.
No footage of a gunman is shown but laughter is repeatedly heard in the background.
The footage was uploaded on YouTube and is tagged “Fishing vessel fijian crew gettin shot, out side fiji waters”.
“At this stage it is too early to make any definite statement about the matter,” Fiji Police Force spokesman Atu Sokomuri told SBS.
“There is no clear evidence to identify the victims as Fijian citizens, nor is there a clear indication of where or when this gruesome incident took place.
“Therefore the Fiji Police Force is seeking the assistance of Interpol and neighbouring police forces to help firmly establish the facts of this case.”
The vessel BI-2353 is registered to the Tching Ye Fishery in Taiwan and its home port is Kaohsiung. The company’s phone number does not answer.
Records on the boat indicate it operates in the West Pacific and Indian oceans.
The YouTube account that uploaded the footage has not responded to messages requesting further details about the footage.