The team, led by Roberto Danovaro from Marche Polytechnic University in Ancona, Italy, found three new species from the Loricifera group.
He told BBC World Service they were about a millimetre in size and looked like jellyfish in a protective shell.
“We plan to go back and see if there are new surprises for us,” he added.
One of the three new Loriciferans (so-called because of their protective layer, or lorica) has already been officially named Spinoloricus Cinzia, after the professor’s wife.
The other two, currently designated Rugiloricus and Pliciloricus, have still to be formally described.
They were discovered in the course of three oceanographic expeditions conducted over a decade in order to search for living fauna in the sediment of the Mediterranean’s L’Atalante basin.
The basin, 200km (124m) off the western coast of Crete, is about 3.5km (2.2m) deep and is almost entirely depleted of oxygen, or anoxic.
Bodies of multicellular animals have been found previously in sediment taken from an anoxic area – or “dead zone” – of the Black Sea, Professor Danovaro told BBC News. But these were believed at the time to be remains of organisms which had sunk there from adjacent oxygenated areas.
What the team found in the L’Atalante dead zone was three species of living animals, two of which contained eggs.
Although it was not possible to extract the animals alive in order to show that they could live without oxygen, the team was able to incubate the eggs in anoxic conditions aboard on the ship.
The eggs hatched successfully in a completely oxygen-free environment.
“It is a real mystery how these creatures are able to live without oxygen because until now we thought only bacteria could do this,” said Professor Danovaro, who heads Italy’s Association of Limnology (the study of inland waters).
“We did not think we could find any animal living there. We are talking about extreme conditions – full of salt, with no oxygen.”
The discovery of the new Loriciferans represents, he said, a “tremendous adaptation for animals which evolved in oxygenated conditions”.
Dead zones in the world’s oceans, he added, were expanding all the time.
Commenting in the journal BMC Biology, Lisa Levin of the Scripps Institution of Oceanography said that before this discovery, “no one had found [animals] capable of living and reproducing entirely in the absence of oxygen”.
“Loriciferans are rarely reported,” she noted.
“Whether they were overlooked or are exceedingly rare and thus not sampled is unclear. Perhaps scientists have been looking for them in all the wrong places.”
Considering the implications of creatures which can exist without oxygen, she said that greater study of animal-microbe interactions in the extreme environment of Earth’s oceans could help answer questions about the possibility of life existing on other planets with different atmospheres.