Around 280 people were rescued off the coast of Lampedusa, with three found dead when the coastguard arrived for the rescue.
Four others died while being taken to Lampedusa, Italy’s southernmost island.
Most of the migrants on the packed boat were from Egypt and Bangladesh, said Italian authorities.
Two coastguard boats conducted the rescue while a boat from Italy’s financial police stood by during "an operation made more complex by the rough sea conditions,” the coastguard said.
Italian authorities said the 65ft wooden boat was in Tunisian waters when the distress call came in, but they were unable to locate the boat.
It was later found in the Italian search-and-rescue area.
The NGO Alarm Phone, which forwards rescue calls from boats carrying migrants to authorities, tweeted that it took Italian rescue boats six hours to reach those in danger.
“Their deaths could have been prevented," the group said.
The International Organisation for Migration marked 2021 as the deadliest for the central Mediterranean crossing route since 2018, with at least 1,315 dead.
Arrivals in Italy this year are significantly higher than the past two winters, totalling 2,051 by early Tuesday, compared with 872 in the same period last year and 835 a year before that.
Arrivals typically peak in the summer months.
More than 23,383 people are missing and presumed dead in the Mediterranean while attempting to make the hazardous crossing since 2014.
Bodies are often not recovered and the deaths are inferred from the accounts of survivors of the crossings.