A man and a 68-year-old woman were pulled alive from the rubble of the collapsed building. Both are seriously injured and were transported by air ambulance to hospitals in the capital.
Four people, including a mother and her daughter, are still missing, Il Messaggero reported.
A 68-year-old man and a 67-year-old woman have also not yet been found, Ansa reported.
The explosion is believed to have been caused by a gas leak in an apartment on the top floor.
The blast shook windows of nearby buildings.
"We had just finished eating and we heard a huge explosion," Rosalba Neri, who lives in the building opposite, told the newspaper.
"We thought a plane had crashed. Then we looked and saw the scene: the building was no longer there and all around were smashed windows, broken glass and damaged cars."
A probe is underway and Rome Mayor Virginia Raggi is on her way to the scene on via Giacomo della Marca, Il Messaggero said.