The island's mayor appealed to the Italian government to deal with the issue after local media reported that many people took to sleeping on mattresses outdoors after the housing centre had filled up.
Several hundred more migrants have reached a tiny Italian island before dawn, swelling to past 2,100 the number of arrivals in some 24 hours.
Italian state radio said four boats arrived at Lampedusa island after being escorted the last miles to port early on Monday by Italian coast guard or custom police vessels.
The 635 latest arrivals followed more than 1,400 who arrived on Sunday.
Human traffickers often take advantage of calm seas to launch unseaworthy boats toward European shores.
The radio said many people slept on mattresses outdoors after Lampedusa’s migrant housing center, which had been empty until Sunday, had filled up.
Hundreds more were being transferred to an unused passenger ferry offshore for quarantine until they can be tested for Covid-19.
Sunday's steady stream of migrant boats arriving at the 20-square-kilometre (about 8-square mile) island, which is closer to northern Africa than to the Italian mainland, was the biggest number of migrants to come ashore in a single day at an Italian port this year.
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1400 migrants have arrived to Lampedusa in the past 18 hours and more are expected, as several boats are in distress off the Maltese coast. Here's my latest piece for @BBCWorld @alarm_phone @SeaWatchItaly @UNmigration pic.twitter.com/7r8MTEa8ml— Sara Monetta (@saramonetta) May 10, 2021
Calls for a naval blockade
Il Giornale di Sicilia, a Sicilian daily, said just before midnight a boat dispatched by the port captain's office aided a fishing boat with 352 migrants aboard, some 16 kilometers (9 nautical miles) from the island.
A few hours later, another coast guard motorboat took aboard 87 men in a boat farther out at sea, while successive hours saw more boats and their passengers reach the island, the newspaper said.
Among them were at least 13 women and eight children, the daily said.
On Sunday, the island's mayor appealed to the Italian government to deal with the sea migrant issue, and national political leaders chimed in, too.
Right-wing anti-migrant leader Matteo Salvini, whose League party is part of Premier Mario Draghi's wide-ranging coalition, is pressing for a huddle with Draghi.
Giorgia Meloni, a far-right opposition leader, insisted that Italy immediately set up a naval blockade to thwart Libya-based traffickers from launching more vessels.
In recent years there have been similar surges in springtime in the number of migrant arrivals.
Several years ago, a few thousand migrants rescued at sea arrived in one day, as more than 100,000 people in some years were plucked to safety from unseaworthy boats, by military vessels, charity ships or cargo vessels.
So far this year, more than 14,000 people have reached Italy's shores.
Last month, a rubber dinghy deflated in the Mediterranean north of Libya, and passengers' phone calls for help, relayed to Libya, Malta and Italy, failed to save them.
About 130 migrants were believed to have perished in that shipwreck.
Italy has insisted, mainly unsuccessfully, that fellow European Union nations take in many of the migrants.
Many are fleeing poverty in their African or Asian homelands and are eventually denied asylum.