The Marine Conservation Society (MCS) said the latest International Council for the Exploration of the Sea data showed cod stocks were only slightly above what are considered sustainable.
MCS fisheries officer Bernadette Clarke said: "Our advice remains to seek alternatives to North Sea cod."
However, the claim has angered Scottish fishing industry leaders.
The MCS's spokeswoman explained: "The efforts of fishers and managers have placed cod in the North Sea on the road to recovery.
"Programmes such as the Conservation Credits Scheme - which rewards fishermen for adopting conservation measures with additional days at sea - together with more effective long-term management plans will hopefully see the fishery continue to recover in the coming years."
But she added: "There are more sustainable cod fisheries that we currently rate as Fish to Eat."
Mike Park, from the Scottish White Fish Producers Association, told BBC Scotland it was time the efforts of fishermen were appreciated and recognised.
Mr Park said: "The advice from the Marine Conservation Society is extremely disappointing."
And Scotland's Fishing Secretary Richard Lochhead said: "All Scottish Cod is caught within internationally agreed limits with the aim of transitioning towards full Maximum Sustainable Yield (MSY) in the very near future, therefore the stock recovery is not being harmed and will not be harmed in any way if people eat Scottish caught North Sea cod."
North Sea cod should stay off the menu for consumers despite evidence of improving stocks, it has been claimed.