More than 600 people attempting to cross the Mediterranean on board a drifting fishing vessel were rescued on Saturday by a merchant vessel and coastguards off Calabria, at the southern tip of Italy.
They were landed in several ports in Sicily.
The authorities also recovered five bodies of migrants who had died in so far undetermined circumstances.
On the island of Lampedusa, some 522 people from Afghanistan, Pakistan, Sudan, Ethiopia and Somalia, among others, arrived from the late hours of Saturday in 15 different boats from Tunisia and Libya.
According to the Italian media, the island's reception center has been overwhelmed.
With a capacity of 250-300 people, it currently hosts 1,200, according to the Ansa news agency.
According to La Sicilia daily, the latest arrivals on Lampedusa came both by ships carrying dozens, even hundreds of people, as well as by small inflatable boats.
Four Tunisians, including one woman, ran aground during the night on the beach of Cala Pisana after crossing the stretch of sea separating Tunisia and the Italian island, the daily said.
At the same time, it said that coastguards had intercepted a 13-meter (43-foot) ship which had departed from the northwestern Libyan city of Zawiya with 123 people from Pakistan, Bangladesh, Egypt and Sudan on board.
NGOs continued to recover hundreds of migrants in distress in the Mediterranean.
SeaWatch reported that it had carried out four rescue operations on Saturday.
"On board SeaWatch3, we have 428 people, including women and children, a woman nine months pregnant and a patient with severe burns," it said on its Twitter account.
Ocean Viking, run by non-governmental organization SOS Mediterranean, said it carried out two rescue operations on Sunday.
First, it recovered 87 people, including 57 unaccompanied minors, who were crammed onto "an overcrowded inflatable boat in distress in international waters off Libya".
Then 108 people, including many women and children, were found in similar conditions.
The NGO said "195 people are now being cared for aboard the Ocean Viking.
The latest inflow of migrants comes at a politically sensitive time in Italy.
Reformist Prime Minister Mario Draghi resigned last week after being toppled by parties in his national unity government.
Italian President Sergio Mattarella has dissolved parliament and set September 25 for new elections to be held.
But Draghi's coalition could be replaced by a government dominated by the eurosceptic Brothers of Italy party and the pro-Russian, anti-immigration League.
Together the two parties are polling at almost 40 percent of the vote.