The latest fishery assessment report by the Secretariat of the Pacific Community highlights the continued overfishing of bigeye tuna.
The 2010 report finds there's no risk of the species going extinct in the western and central Pacific.
But it warns the amount of bigeye fishing there must decrease by at least 32 percent from the average levels for 2006 to 2009 to ensure long-term sustainability.
The SPC has assessed the trends and current stocks of the four tuna species mainly targeted by fishers: skipjack, yellowfin, bigeye and south Pacific albacore.
The report states that yellowfin, skipjack and south Pacific albacore stocks are reasonably healthy.
But the report also recommends that the yellowfin catch in the western equatorial Pacific be limited to current levels and that limits on skipjack fishing be considered.