The PNA is made up of the island nations that control the bulk of the Pacific's purse seine fishery.
The Western and Central Pacific Fisheries Commission, or Tuna Commission, met last week in Hawaii and the PNA's chief executive, Ludwig Kumoru, said they were happy with what had been achieved.
He said a critical element of this was maintaining the Tropical Tuna Measure through which bodies such as the PNA aim to keep the tuna take sustainable.
Dr Kumoru said the Americans had been pushing for more fishing days.
"But they agreed not to push that element to increase catch and also the Hawaiian fleet was proposing to increase their catch by another 1,000 metric tonnes, but that has been put off too.
"Science is saying that big eye is OK but some of us still think these results just came last year, let's give it some more time to really see what is going on."
Dr Kumoru said they had also made some progress over transshipping.
The PNA, along with the the Forum Fisheries Agency, had both been pushing for transshipping to be done in port so that the practice can be properly monitored.
Ludwig Kumoru said at the moment it was very difficult to see what was happening on the high seas.
"There is very little supervision on what's going on. So there have been proposals that we should have observers, even on the carrier boats. With the carrier boats you can see whatever boat comes into contact.
"So there has been, I think, a positive way forward and then we can make some decisions on that too. There is general agreement that we should put transshipment under control now."