Two more species of tuna have been added to the Red List of Threatened Species.
They join the Southern bluefin tuna - listed as critically endangered.
The report, published in this week's Science, is the first global assessment of this highly prized family of fish, which are at risk of being over-fished.
The World Conservation Union (IUCN) says there is a lack of resolve to protect against overexploitation driven by high prices.
Until this latest study, attempts to assess the health of scombrid and billfish populations, families of fish that include tuna and swordfish, have been carried out at a regional scale.
This study, which relies on the IUCN Red List criteria to judge the stocks' health, took a more global approach.
Of the 61 species of fish assessed, seven were earmarked as either vulnerable, endangered or critically endangered. All suffer from over-fishing, habitat loss and pollution.
Along with the two species of tuna, two mackerel and two marlin joined the Red List.
The 'sapphires of seafood'
Per kilo, bluefins are among the most expensive seafood in the world.
"All three bluefin tuna species are susceptible to collapse under continued excessive fishing pressure. The Southern bluefin has already essentially crashed, with little hope of recovery," said one the the study's authors Kent Carpenter the IUCN's Marine Biodiversity manager.
Southern bluefin numbers have reached levels that are one twentieth of those recorded before industrial fishing began.
Atlantic bluefins have probably gone the same way, add the authors, while bigeye tuna is labelled "vulnerable".
"Tunas are highly migratory fish, swimming across ocean basins and between the waters of various countries during their lifetimes. Conserving them requires regional and global co-operation," commented Susan Lieberman, director of international policy with the Pew Environment Group in a statement.
What is more, tuna's restricted spawning grounds make them exceptionally susceptible to collapse if over-fishing continues, reports the international team of scientists.
And tuna's long lifespan means it would take their population several years to recover if fishing stopped altogether.
Pew's Dr Lieberman adds: "The IUCN Red List assessment reinforces that it is time for governments to live up to their responsibilities."
The report comes days before the tuna regional fisheries management organizations (RFMOs) assemble in in La Jolla, California for the Kobe III meeting.