The survivors, all male Syrian nationals, were picked up from a semi-sunken boat about 10 nautical miles (18.5km) southwest of Lampedusa, a statement said.
They told rescuers they had set off on Sunday (local time) from Libya, and that 21 of the 28 people they had aboard, including three children, had fallen into the sea during rough weather.
The coast guard said it had taken the survivors to Lampedusa and had deployed naval and air units to look for the missing people.
The Italian office of UN refugee agency UNHCR told Reuters that Sudanese people were also on the boat, which is believed to have departed from the port of Sabratha, west of Tripoli.
The head of UNHCR Italy, Chiara Cardoletti, wrote on X that the survivors were in "critical" condition and had lost relatives at sea.
The boat "capsized repeatedly, leaving people clinging to the side of the boat as their family members drowned around them," Nicola Dell'Arciprete, UNICEF country coordinator for Italy, said in a statement.
The central Mediterranean is among the world's deadliest migration routes. According to the UN migration agency, more than 2500 migrants died or went missing attempting the crossing last year, and 1047 this year, as of Tuesday.
The latest figures from the Italian interior ministry recorded that just over 43,000 migrants had reached Italy so far in 2024, well down from previous years.
