Foreign fishing vessels catching bigeye tuna and yellowfin tuna in the central and western Pacific are being urged to agree to cut catches to preserve stocks.
The Tuna Commission, which manages the area, is meeting in Busan in South Korea.
Scientists for the commission say the high grade tuna are under pressure and recommend catches be reduced by 30% over the next three years.
Ministry of Fisheries international policy manager Matthew Hooper, who is at the meeting, there is a need for urgent action after talks failed last year.
"Both fisheries have got to the point where any further increases in fishing effort will likely drive those stocks into an overfished state."
The commission has members from both the Pacific Islands and the so-called distant water fishing nations including Japan, Taiwan, Korea and China as well as Canada and the United States.
Commission director Andrew Wright says they want to be able to track the activities of the big factory ships, and there is a strong move to develop a regulation to provide the relevant data.