The Italian coastguard is carrying out two large-scale operations to rescue around 1,200 migrants from overcrowded boats off the coast of Sicily.
About 800 people are travelling on one of the fishing boats, while around 400 are on another.
The country’s coastguard has already rescued around 2,000 people in other operations since Friday.
At least two people died during the weekend’s boat crossings, German non-profit ResQship said.
Migrant arrivals to Italy have risen steeply compared with the same period last year, despite efforts by the right-wing coalition government to clamp down on irregular migration.
The boat carrying 400 people, which is believed to have set out from Tobruk in Libya, was still without help late on Monday evening, according to an unofficial hotline for migrants in distress, Alarm Phone.
It said it had raised an urgent alarm with the authorities of Italy, Greece and Malta on Sunday.
German non-governmental organisation Sea-Watch International said two merchant vessels near one of the ships had been ordered not to help with rescue efforts by Malta while the boat was in Maltese waters. Instead, one of the ships had been allowed to supply it with fuel and water. The Maltese government has not commented on the matter.
Alarm Phone said that it had been in contact with people on board the boat, which is now in Italian waters south-east of Capo Passero. It said the boat was adrift and taking on water on Sunday. A woman on board also said it was without its captain and had several people in need of medical care.
An operation to rescue the 800 people on the other boat is also under way south-east of Syracuse, but the operation has been complicated by overcrowding on board, the Italian coast guard said. It was not immediately clear where the boat had set out from.
Other boats arrived at the Italian island of Lampedusa, one of the main arrival ports for people wanting to reach Europe, over the weekend.
At least two migrants died and around 20 others were missing after their boat sank on Saturday night, ResQship said.
According to monitoring group IOM Missing Migrants Project, more than 26,000 people have died or gone missing at sea in the central Mediterranean since 2014.