The Italian coast guard also transported to Lampedusa another 49 people on Saturday from Banksy's rescue ship Louise Michel.
Authorities on the Italian Mediterranean island of Lampedusa are calling for urgent help after mass migrant arrivals over the weekend pushed its hotspots to the brink of collapse.
"Lampedusa is no longer able to cope with this situation," mayor Totò Martello told Italian news agency ANSA.
"Either the government takes immediate decisions or the whole island will go on strike. We cannot manage the emergency and the situation is now really unsustainable," he said.
Around 370 migrants disembarked on Saturday night on the southern Italian island.
Their boat was spotted off the coast by the Italian Coastguard and was at risk of sinking due to strong winds.
The migrants, whose nationality is not yet known, disembarked in small groups before undergoing coronavirus tests and being transferred to a reception centre.
Italy's coastguard on Saturday also transported 49 vulnerable migrants, mainly women and children, from Banksy's "Louise Michel" rescue ship.
Another 500 migrants arrived on the overburdened island on Friday on "around 30 small boats mainly from the Tunisian coast", news agency AFP said quoting Italian media.
Lampedusa now reportedly houses around 1,160 migrants, six times the amount of its maximum capacity.
Earlier this week Sicily's governor Nello Musumeci ordered the closure of all migrant centres in the region after camps became too crowded to maintain social distancing measures and some migrants tested positive for COVID-19
"Sicily cannot continue to pay [for] the indifference of Brussels and the silence of Rome", he said.
The decision was later overturned by a local administrative court (TAR).
Migrants killed in migrant ship fire
Italian state TV channel RAI reported that four migrants died after a fire broke out on a migrant sailboat on Sunday.
The blaze was reportedly sparked by fuel on the vessel, which caused an explosion that sent up a column of smoke that could be seen by bathers at a beach near Crotone, in the southern region of Calabria.
It is unclear whether the death were caused by the fire or by drowning. Other migrants are reportedly missing at sea.
Many of them were injured, RAI reported, while two Italian Coast Guard officers suffered burn and leg injuries.
LaPresse news agency said the vessel had about 20 migrants aboard.