EU countries should take in refugees under a quota scheme, according to a European Commission proposal.
According to the UN, 60,000 people have already tried to cross the Mediterranean in 2015.
Migrants are being driven to make the journey by “horrific abuse” in Libya, Amnesty International says.
More than 1,800 migrants have died in the Mediterranean only in 2015, a 20-fold increase on the same period in 2014.
The European Commission’s migration policy, to be announced on May 13, will also propose organizing legal means for migrants to come to Europe so they do not turn to traffickers.
However, it will need to be agreed by EU states.
European leaders will discuss the proposals at a summit at the end of June.
The measures proposed by the European Commission are the latest in a series of steps designed to stop migrants drowning in the Mediterranean.
More than 200,000 migrants fleeing conflict or poverty from countries such as Syria, Eritrea, Nigeria and Somalia are estimated to have crossed the Mediterranean in 2014, with thousands dying making the journey.
Quotas would be determined using a number of factors, including a country’s population, economic indicators and the number of asylum seekers previously accepted.
Germany keenly supports the idea of quotas, having received 200,000 asylum applications in 2014.
Countries such as Italy and Malta, where large numbers of migrants arrive by boat, have also called for EU members to share responsibility for migrants more evenly.
Austrian Chancellor Werner Faymann has described a quota as “a question of fairness”, adding that asylum is “not an act of mercy but a human right”.
However, other EU countries are fiercely opposed to the idea of quotas.
Leaders in Hungary, Slovakia and Estonia have also objected to a quota system, with Hungarian PM Viktor Orban calling it “a crazy idea”.