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 centre 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-metre (43-foot) ship which had departed from the northwestern Libyan city of Zawiya with 123 people from Pakistan, Bangladesh, Egypt and Sudan on board.
Most dangerous route
Offshore 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.
OceanViking, operated by non-governmental organisation SOS Mediterranean, reported that it had recovered 87 people, including 57 unaccompanied minors, who were crammed onto "an overcrowded inflatable boat in distress in international waters off Libya".
The Central Mediterranean migration route is the most dangerous in the world.
The International Organization for Migration estimates that 990 people have died and disappeared since the beginning of the year.
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.
In a tweet on Sunday, Matteo Salvini, leader of the League, deplored 411 illegal migrants having arrived in a few hours on Lampedusa.
"On September 25, Italians will be able to finally choose change: for the return of security, of courage and of border control," he wrote.