Professor Glenn Hurry said bluefin and bigeye tuna should no longer be harvested, as stocks were dangerously depleted.
He also warned "serious action" needed to be taken to reduce the yellowfin tuna catch.
"Yellowfin tuna's down to about 38 per cent of its original spawning biomass," said Professor Hurry, the outgoing executive director of the Western and Central Pacific Fisheries Commission (WCPFC).
"Bigeye tuna's down now to about 16 per cent.
"In any sense in a well-managed fishery you'd actually stop fishing on that and begin to rebuild the stocks."
Professor Hurry said the situation for bluefin tuna was even more dire, with the Pacific population at "3 or 4 per cent of its original spawning biomass".
"It's at a level where you shouldn't be fishing," he said.
He said the key problem was that there are too many vessels – at least 300 - equipped with sophisticated radar, chasing the schools of tuna.
He said the optimum number of fishing boats was passed 10 years ago.
Any trans-Pacific action to stop or limit the catch would require an agreement between the 33 countries and participating territories which make up the WCPFC, which next meets in Samoa in December.
Island nation Palau joins fight against overfishing
The president of one of the WCPFC's smallest members, Palau, has decided the time to act is now – with or without support from other nations.
"We have to take drastic steps," president Tommy Remengesau Junior said.
"There are species of bluefin and species of bigeye tuna that are dangerously close to becoming unsustainable. Those are the hard facts that we have to look at."
Mr Remengesau is proposing to ban all foreign fishing in Palau's exclusive economic zone, which extends 200 nautical miles out from shore and covers an area the size of New South Wales.
In its place he wants to create a domestic commercial fishing industry with access to one-fifth of Palau's waters.
"Our policies are geared towards future sustainability of our resources and the food security of our tourism and local demands," Mr Remengesau said.
"Palau wants to maximise whatever we can do, not just for our own interest, but because the fish is migratory we would be doing our share of ensuring that the stock, when they come to Palau, it's like a rest area or a replenish area."
The tiny Micronesian nation, with a population of just 21,000 people, already has an international reputation for taking a lead on marine conservation.
In 2009 it declared the world's first shark sanctuary in a bid to stop the practice of shark-finning.
There are now 10 sanctuaries across the globe which outlaw the killing of sharks.
Palau's president says his country is not receiving fishing profits
Map: Palau's 200 nautical mile Exclusive Economic Zone
Palau's reefs have become a mecca for scuba divers and snorkellers. Tourism is the country's main industry, pulling in about $85 million a year.
But fishing is Palau's second-biggest earner, with taxes and levies on foreign fishing fleets providing about $5 million a year.
Mr Remengesau, however, believes his county and many other Pacific nations are not getting a fair share of the Western and Central Pacific fishery, which is worth $6 billion per year.
"The funding that we get from the fisheries is very minimal," Mr Remengesau said.
"A drop in the bucket. Certainly it is not representative of the fact that (tuna) is a billion-dollar industry throughout the Pacific.
"A recent study shows that it's really 94 per cent of the total value of the tuna which is realised by the outside industry, and only 6 per cent actually is returned to the local government and to the people who are the resource owners."
Professor Hurry said fishing companies could reap huge profits.
"During the peak period when tuna was $US2,300 a tonne, a vessel taking 15,000 tonnes of tuna a year was probably making $US20 million a year, net profit, over and above cost," he said.
"There's very few other businesses in the world where you're going to make that level of profit."
Aerial surveillance 'needed to catch illegal fishermen'
Mr Remengesau said there was no economic benefit for his country when foreign vessels fish in Palau's waters.
"There's no trickling down of economic benefits. They’re not coming in to buy fuel, they’re not hiring our people, they’re not buying their supplies here," he said.
"There are no canneries on land for their products. In fact we believe some are engaged in illegal activities, offloading their catch outside so they're not reporting accurately what they catch."
Royal Australian Navy Lieutenant Commander Alan Willmore, Palau's maritime surveillance advisor, said: "I reckon we have managed to catch about 10 per cent of the vessels operating illegally."
Some of the illegal fishing trade is generated by vessels based in Palau's capital, Koror.
"We're finding that the licensed vessels here in Palau go out, and they fish as normal, as would be expected, and then they rendezvous with an illegal vessel from either Taiwan or another country and they offload fish to that vessel until that vessel is full," Lt Commander Willmore said.
"That vessel leaves Palau's economic zone and transits back to their country. The licensed vessel will fish until full and then come back to Palau and everything looks very innocent."
The process of transhipping fish is costing Palau millions of dollars every year in lost revenue.
Palau has only one patrol boat, supplied by Australia, to monitor the far reaches of its waters, plus two smaller vessels donated by the Nippon Foundation of Japan.
But Lt Commander Willmore said without comprehensive aerial surveillance it is difficult to catch "the bad guys which we are most interested in".
The United States has been testing the use of Cessna aircraft fitted with radar to patrol Palau's waters.
President Barack Obama's counsellor John Podesta visited recently and was briefed by Lt Commander Willmore and others about the merits of aerial tracking of fishing vessels.
Palau's president will face a challenge getting political support at home to legislate for a wider marine sanctuary, but is confident of success.
Professor Hurry is not so certain of success on a regional front.
But he said tough decisions must be made by members of the Western and Central Pacific Fisheries Commission and the fishing industry if "the world's last great fishery" is to survive.