By Alex Kirby
BBC News Online environment correspondent
Turtles, dolphins and sharks are among the unintended victims of Mediterranean fishing fleets, the World Wide Fund for Nature warns.
Dolphin: One victim of the nets
Driftnets which hang beneath the water and trap anything which happens to swim into them are to blame, it says.
It believes that in some parts of the sea so many dolphins are killed that their survival in the region is threatened.
The conservationists want the European Union to act to ban such fishing nets.
Accidental annual catch
The WWF has published a report, Biodiversity Impact Of The Moroccan Driftnet Fleet In The Alboran Sea.
Driftnet fishing was banned by the EU from 1 January 2002, while the UN adopted a moratorium on large driftnets 10 years earlier.
The report says the nets used in the Mediterranean are anywhere from seven kilometres (4.75 miles) long to twice that size.
It also says the Moroccan driftnet fleet, with 177 boats, is "the most lethal for Mediterranean marine biodiversity".
The WWF estimates the accidental annual catch of striped and short-beaked common dolphins in the Alboran Sea, in the south-west Mediterranean, is 3-4,000.
The dolphins were included on the Red List of Threatened Species published on 18 November by IUCN-The World Conservation Union.
The WWF says that the catch figure is more than 10% of the area's dolphin population.
Total ban requested
The WWF also thinks a further 13,000 animals are being caught every year around the Straits of Gibraltar and in nearby areas.
It says the Moroccans are far from the only fleet to blame, with "Italian, French, Turkish and most probably other fishing fleets using driftnets in breach of existing legislation."
Paolo Guglielmo of WWF's Mediterranean programme said: "The evidence we have gathered on the Moroccan fleet brings us to think that illegal driftnet fishing currently happening in the whole Mediterranean results in a massive slaughter of vulnerable species. More than 4,000 km of illegal nets are ensnaring all that gets in their way."
WWF believes the Moroccan fleet catches about 23,000 sharks in the Alboran Sea, and 77,500 more in neighbouring waters.
The Moroccans go after swordfish: one estimate suggests that for every two they catch, one shark also dies. Another key marine species caught in the driftnets is the loggerhead turtle.
Dr Simon Cripps, of WWF's endangered seas programme, said: "The only way to prevent the massacre of marine species caused by these driftnet fleets is to make the Mediterranean a driftnet-free sea by enforcing a total ban on all the driftnet fisheries in the region. The EU must urgently help all Mediterranean countries put in place plans to convert their driftnet fleets."
WWF wants the EU to monitor and prosecute all member state fleets which use the nets, and wants non-EU countries, especially those in North Africa, to ban them.