Thirteen people were wounded, including seven children, two of whom are in critical condition.
“In this hour of pain, my condolences go to the victims’ families together with thoughts for the wounded and their dear ones,” the prime minister wrote on social media.
Meloni also thanked firefighters for their “prompt” intervention and “those who are cooperating in rescue operations”.
The victims are a 29-year-old man and a 35-year-old woman.
Naples Mayor Gaetano Manfredi on Tuesday announced a day of mourning on the day of the victims’ funeral.
Health officials at the Santobono hospital in Naples said two of the children injured in the incident are in critical condition.
The two kids, aged seven and four, sufferd multiple head injuries.
They are being treated in the intensive care unit of the Santobono.
Meanwhile, prosecutors have opened an investigation into the collapse.
Naples State attorneys are waiting for the first technical results of inspections following the collapse, investigative sources said.
The 800 residents - including 300 children - of the Vela Celeste (Sky Blue Sail) building where the collapse took place have in the meantime been evacuated.
Tents have been set up to aid the evacuees.
In Scampia, several other ‘Sails’ apartment buildings have been torn down over their state of decay.
A ‘restyling’ of the area, which is trying to make a civic comeback after years of being identified with the Camorra mafia and drug pushing, has started.
The municipal administration announced in April renovation work on the Vela Celeste to be funded under the Piano Periferie (suburbs plan) with some 18 million euros.
The Sails were an iconic backdrop in the hit Camorra TV show Gomorra (Gomorrah), based on Roberto Saviano’s expose’ of the same name.
ANSA