The man was pulled out of the rubble alive over 10 hours after the collapse. He went into cardiac arrest and could not be revived when he reached the hospital, Italian media reported.
"I express deep sorrow and condolences, on behalf of myself and the government, for the tragic loss of Octay Stroici, the worker who was killed in the collapse of the Torre dei Conti in Rome," Italy's Prime Minister Giorgia Meloni said in a statement.
"​We are close to his family and colleagues at this time of unspeakable suffering."
Parts of the 29m Torre dei Conti crashed to the ground on at least two occasions, videos posted on social media and Reuters video showed.
Clouds of dust came billowing out of the windows, along with the sound of collapsing masonry.
The second incident took place while firefighters were working on the structure with aerial ladders.
A second worker, also Romanian, was pulled out almost immediately and hospitalised with serious but not life-threatening head injuries, while two more workers suffered minor injuries and declined hospital treatment.
None of the firefighters were injured.
Authorities have seized the construction site, Italian daily Corriere della Sera reported.
The tower, which was due to be converted into a museum and conference space, is located halfway along the Via dei Fori Imperiali, the broad avenue that leads from central Piazza Venezia to the Colosseum.
The building was still standing, but showing significant internal damage.
It once hosted city hall offices but has not been in use since 2006 and was being worked on as part of a four-year renovation project due to end next year, according to Rome city authorities.
Due to the EU-funded restoration work, the area around the tower was closed off to pedestrians.
The building was erected by Pope Innocent III for his family in the early 13th century, and was originally twice as high, but was scaled down after damage from earthquakes in the 14th and 17th centuries.
Before the latest renovation phase was started in June, structural surveys and load tests were carried out "to verify the stability of the structure, which confirmed the safety conditions necessary" to proceed with work, including asbestos removal, officials said.
The work, carried out at a cost of 400,000 euros ($A704,364), was just about complete.
with AP and DPA
11°C