More than 2,100 migrants arrived on an Italian island over the weekend, Italian media reported, while hundreds more were in trouble in Maltese waters according to an NGO.
Several hundred more migrants reached Lampedusa before dawn on Monday, following more than 1,4000 who arrived on Sunday.
Many people reportedly slept on mattresses outside Lampedusa's busy migrant housing centre.
Italian news agencies said around 400 migrants arrived on a single ship, while another 20-metre boat carrying 325 people was intercepted 13 km off the coast of the island.
Sunday saw the largest number of migrants coming ashore in a single day at an Italian port this year.
The NGO Alarm Phone, which runs a hotline to rescue migrants, has appealed for help to collect passengers from five boats carrying more than 400 people off Malta. "The situation on board is critical...A rescue is needed now,” it said.
Sicilian judicial authorities meanwhile renewed a ban on any intervention at sea by the rescue ship Sea-Watch 4.
The German NGO ship - which had to keep it at anchor in the port of Palermo, Sicily for six months - is now banned until March, after an inspection found too many life jackets on board in relation to its size.
Members of the NGO believe that the inspection was a backdoor way for the authorities to block the vessel and prevent it from rescuing migrants at sea.
"We hope the authorities will not prevent us from going to the central Mediterranean with the same absurd accusations we are used to," Sea-Watch Italy tweeted on Friday after returning from its latest mission.
Another ship, Sea-Watch 3, was blocked in March by the coastguard at the Sicilian port of Augusta, again citing security concerns.
Some 530,000 migrants have reached Italian shores since the beginning of 2015, according to the International Organization for Migration (IOM), an intergovernmental organisation based in Geneva.
Between 1 January and 21 April 2021, 8,604 people arrived in Italy and 65 in Malta, while 359 died en route, according to IOM.
Human traffickers often take advantage of calm seas to launch unseaworthy boats toward European shores.