At least 24 migrants trying to reach Europe from Africa died after their boat sank in the Mediterranean, the Italian navy said on Tuesday after completing a two day search for bodies.

A further 364 migrants were rescued by navy and coastguard vessels after the fishing boat capsized on Sunday evening, the latest in a series of similar shipwrecks.

Two days earlier, another boat carrying migrants sank near the Libyan coast leaving around 250 feared drowned.

Droves of people, many fleeing war in Syria and military conscription in Eritrea, have attempted the perilous passage this year, pushing the number of seaborne arrivals in Italy to a record of more than 100,000.

Despite calmer summer seas, the rickety boats departing North Africa, where a breakdown of order in Libya has been exploited by traffickers, often run into difficulty. The navy said on Monday it had rescued almost 4,000 migrants over the weekend.

The record numbers of arrivals are straining the resources of Italy's coastguard and navy, which last October launched its "Mare Nostrum" or "Our Sea" search and rescue mission after a shipwreck which killed 366 people near the Italian coast.

The mission has many political opponents in Italy but authorities say it has saved tens of thousands of lives. It involves Italian vessels patrolling the Mediterranean looking for boats in distress and bringing the migrants to shore.

However, Italy says it can no longer face the problem of sea-borne immigration from Africa on its own and it should be tackled jointly by the European Union.

Interior Minister Angelino Alfano and European Union Home Affairs Commissioner Cecilia Malmstrom are due to meet in Brussels on Wednesday to discuss the issue.

The surge in migrants has also helped revive support for the anti-immigrant Northern League party. Alfano warned on Sunday that an "ugly extreme right wing" was emerging in Italy.

Prime Minister Matteo Renzi has called for the European Union to address the crisis by beefing up the resources of Frontex, the EU's border control agency. He has also called on the United Nations to secure the border of Libya, from where the vast majority of boats depart for Europe.