Campaigners have accused Tesco of stocking a brand of tuna that is caught in a way that can harm other wildlife.
Greenpeace said the supermarket giant pledged in 2012 to ensure all its own brand tuna was sustainably caught.
But the group says Tesco has started to stock tinned tuna from low-cost brand Oriental and Pacific which it says is caught in large nets.
Tesco said Greenpeace was 'simply wrong' and the manufacturer said it 'totally refutes' the claims.
Greenpeace claimed the brand was 'dirty' because tuna in it was caught in big nets, known as purse seines, that could kill sea creatures.
The environmental group said Tesco 'must try harder' to make sure tinned tuna was sustainably caught.
Greenpeace said Sainsbury's was at the forefront of sustainable tuna, and Waitrose, the Co-operative, Marks and Spencer, and Morrisons were also praised.
Ariana Densham, Greenpeace UK oceans campaigner, added: 'Morrisons joins Sainsbury's as a market leader on tuna sustainability. They have eliminated unsustainable tuna from their products, which is great news for sharks, turtles and rays.
'If Tesco wants to catch up with the front runners and win back consumer confidence, they must take this dirty tuna off their shelves today.'
Campaigner and celebrity chef Hugh Fearnley-Whittingstall, who is featuring the issue on his Fish Fight programme on Channel 4 on Sunday, called on Tesco to take the brand off its shelves.
Tesco said it had moved much faster than many of its competitors to make sure its own-brand tuna was 100% caught using a pole and line, which avoids catching other species by accident.
It said it had also promised to use sustainable tuna in other products such as pastas, sandwiches and salads.
A spokesman said: 'Many of our competitors continue to sell non-pole and line caught tuna. Customers have a great choice of sustainable tuna at Tesco.'
LDH, which owns the Oriental and Pacific (O&P) tuna brand, supplies a range of products including canned tomatoes, fish, fruit and vegetables, and dried pasta.
In a statement, the company said: 'At least 85% of the tuna we sell is fished using the pole and line method; our O&P brand skipjack tuna is caught using the purse seine fishing method, which accounts for 63% of all tuna caught around the globe.
'Credible scientific research by the Regional Fisheries Management Organisations shows that stocks of skipjack tuna are healthy.
'All of our tuna suppliers are members of the International Seafood Sustainability Foundation and support its research-led initiatives for long-term conservation of tuna stocks.'