The group entered the water at Vaavu Atoll on Thursday morning and were reported missing when they failed to resurface later on.
Police said the weather was rough in the area, about 100km (62 miles) south of the capital, Male, when the group went missing. A yellow warning was issued for passenger boats and fishermen.
Shareef said the group had permission to study the coral, including deep dives, but added that there was no mention of the cave in their proposal.
Shareef confirmed that Montefalcone’s team did have a permit for their scientific work, valid until Sunday, which allowed them to descend to 50 metres.
The mouth of the cave is 47 metres below the surface.
The permit covered various atolls, including Vaavu, with the Duke of York named as the dive boat.
However, only three of those who died were listed as researchers. Neither Sommacal nor Benedetti were mentioned.
The University of Genoa told the BBC that it did not give approval for any kind of deep-sea dive as part of the team’s scientific research.
“The requests submitted to the Maldivian authorities…were evidently made outside the scope of the mission authorised by the University,” a spokesperson said.
They underlined that the dive was carried out “in a personal capacity”, and not part of the research.
