Other security officials said that the cause of the explosion was not known.
"We're investigating the cause. We don't know whether it was a terrorist attack or something else," Ali al-Maliki, the head of the security committee in the Basra council, said.
Hussein Talib, a member of parliament for Basra, hinted that the blasts could have a more sinister cause.
"As a lawmaker from Basra I hold the military and police leadership responsible for the blood that has been shed," he said.
"They are not responding to the people of Basra. We want the police of Basra to be responsible for security in Basra and we have constantly been repeating this request."
Private communal generators are common in Iraq, where demand for electricity dramatically outstrips supply, forcing the use of unpopular power rationing.
Electricity shortages triggered protests across the country over the summer, including in Basra, that eventually led to the resignation in June of the electricity minister.