Despite a collapse of world tuna stocks, the Australian Government has decided not to support a global ban on the trade of the northern variety of the species.

Instead the Federal Environment Minister, Peter Garrett, is supporting stronger trade control measures on the trade of Atlantic bluefin tuna.

Australia will formalise its position at the 175-nation Convention of the Parties to the Convention on International Trade in Endangered Species (CITES) which starts in Doha tomorrow.

Stocks of Atlantic bluefin tuna are estimated to be at 15 per cent of the original 1940s levels after decades of industrial-scale fishing.

Mr Garrett says he believes imposing a blanket prohibition on international trade would undermine international fisheries management and cooperation to protect the species.

He says it will also allow individual countries to continue to catch Atlantic bluefin tuna for domestic consumption.

Greenpeace and the wildlife trade monitoring group Traffic say the stocks of Atlantic bluefin tuna are so low the species should not be fished at all.

Watch the full story on ABC1's Lateline tonight at 10.45pm AEDT.