Italy's coast guard said it was trying on Monday to rescue 1,200 more migrants aboard two boats on the Mediterranean Sea after saving about 2,000 already over the weekend.

The rescue of about 800 migrants aboard an overloaded fishing boat was ongoing, the coast guard said.

The boat was located in Italian waters more than 120 miles (190 kilometres) southeast of Syracuse, in Sicily.

The operation -- involving three patrol boats and a merchant ship, all coordinated by the "Nave Peluso" coast guard boat -- was described as "complex" due to the overcrowding.

A second fishing vessel carrying 400 migrants and also in Italian waters had been intercepted by the coast guard ship "Diciotti" 170 miles southeast of Capo Passero, at the southernmost tip of Sicily.

Two merchant vessels were assisting in that rescue, the coast guard said.

Alarm Phone, a hotline used by migrants in distress, said on Twitter on Monday that the people onboard were "in panic".

Alarm Phone tweeted on Sunday that, according to a woman onboard, the boat that had set off from Libya was missing its captain, and several people onboard needed medical care, including a child, a pregnant woman and a disabled person.

Three people in distress had jumped overboard and one fell unconscious, it wrote.

The coast guard said that besides the ongoing operations about 2,000 people had been saved since Friday in "a large number of rescues".

Thousands of migrants have landed on Italy's shores, especially the island of Lampedusa, in recent days after making the dangerous journey aboard flimsy vessels from North Africa.

On Sunday, German aid group ResQship said at least two migrants had died and about 20 others were missing after their vessel sank overnight Saturday to Sunday after leaving Tunisia.

ResQship told AFP its charity boat had rescued 22 people from the shipwreck and took them to Lampedusa, helped by "good cooperation" with the Italian coastguard.

According to interior ministry figures, more than 14,000 migrants have arrived in Italy since the beginning of the year -- significantly more than the 5,300 who had arrived over the same period in 2022 and the 4,300 during 2021.