Several hundred more migrants reached a tiny Italian island before dawn on Monday, swelling to more than 2,100 the number of arrivals in some 24 hours.
Italian media reported four boats arrived at Lampedusa island after being escorted the last miles to port early on Monday by Italian coast guard or police vessels.
The 635 latest arrivals followed more than 1,400 who arrived on Sunday.
Video showed hundreds of migrants stranded and waiting at the Lampedusa port on Monday.
Human traffickers often take advantage of calm seas to launch unseaworthy boats toward European shores.
Media reports said many people slept on mattresses outdoors after Lampedusa's migrant housing centre, 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.
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.