After record arrivals from 2014 to 2016, the European Union's deal with Turkey to stop arrivals to Greece and blocks on migrants inside Libya and off its coast have greatly reduced the flow, the International Organization for Migration (IOM) said.
Professor Philippe Fargues of the European University Institute in Florence, author of the report, said the figures probably underestimated the actual scale of the human tragedy.
"The report states that at least 33,761 migrants were reported to have died or gone missing in the Mediterranean between the year 2000 to 2017. This number is as of June 30," IOM's Jorge Galindo told a Geneva news briefing.
"It concludes that Europe's Mediterranean border is by far the world's deadliest," he said.
So far this year some 161,000 migrants and refugees have arrived in Europe by sea, about 75 percent of them landing in Italy with the rest in Greece, Cyprus and Spain, according to IOM figures. Nearly 3,000 others are dead or missing, it said.
"Shutting the shorter and less dangerous routes can open longer and more dangerous routes, thus increasing the likelihood of dying at sea," Mr Fargues said.
The report said: "Cooperation with Turkey to stem irregular flows is now being replicated with Libya, the main country of departure of migrants smuggled along the central route; however, such an approach is not only morally reprehensible but likely to be unsuccessful, given the context of extremely poor governance, instability and political fragmentation in Libya."
On Friday, Libya's EU-backed coastguard intercepted more than 600 mainly sub-Saharan African migrants, including many women and children, from a total of five boats that had left from the coast east of the Libyan capital, Tripoli, coast guard officials said.
On Wednesday and Thursday, Italy's coast guard said some 1,600 migrants were rescued from nearly 20 vessels in the central Mediterranean.
Libya's U.N.-backed government said on Thursday it was investigating reports of African migrants being sold as slaves and promised to bring the perpetrators to justice.
Footage broadcast by CNN appearing to show African migrants being traded in Libya sparked an international outcry and protests in Europe and Africa.
(Reporting by Stephanie Nebehay, Hani Amara and Steve Scherer; Editing by Hugh Lawson)