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One News said information on the video suggested it was filmed outside Fiji waters, but it was yet to verify the authenticity of the video.
Three men are shown holding on to an upturned boat before being shot.
3 News reported it had tried to establish whether the video was authentic and that Fiji police were investigating.
The video appeared to have been filmed from the deck of a large vessel. Three men are shown holding on to an upturned boat in the water before being shot.
3 News reported that a Fiji Government official insisted the video did not show local fishermen.
New Zealand's Ministry of Foreign Affairs and Trade has been alerted.