Italy coordinated the rescue of 2,600 migrants off Libya, three years to the day after 366 people died in a sinking that first alerted the world to the Mediterranean migrant crisis.

Numerous children were among those saved from distressed vessels on Monday, including 700 who had been crammed onto a fishing boat, the coastguard said.

Two women and a child had to be evacuated for medical treatment after suffering severe burns caused by spilled fuel during a rescue from a rubber dinghy by a boat operated by the Doctors without Borders (MSF) charity.

In the disaster three years ago, a fishing boat packed with some 500 people caught fire and sank rapidly in darkness just off the outlying Italian island of Lampedusa in the night of October 2-3.

A total of 366 bodies were recovered in the hold or washed up on the coast of an island where Pope Francis had, a few months previously, railed against the "globalisation of indifference" towards the plight of migrants seeking better lives in Europe.

The disaster resulted in Italy's navy launching a large-scale search and rescue operation that has since evolved into a multinational effort involving groups like MSF and Save the Children.

Hundreds of thousands have been rescued but at least 11,000 people have drowned in the Mediterranean since the Lampedusa tragedy, according to figures collated by the UN refugee agency.

Italy last year declared October 3 a national day of commemoration and welcome in honour of the dead.

A commemorative march was held on Lampedusa on Monday with 200 youths from all over Europe and relatives of some of the victims taking part.