"This is a tragedy, no doubt about it, especially on the heels of the tragedy in Fort Hood that is on our minds," Demings said.
"I'm just glad we don't have any more fatalities or any more injuries than we currently have."
Every person who was shot was in the offices of Reynolds Smith and Hill, on the eighth floor of the building. The five survivors were in stable condition, Demings said.
Charles W. Price, an attorney who represented Rodriguez in a bankruptcy case, declined to comment on the incident.
Mike Bernos, a spokesman for the engineering firm, said that Rodriguez was an entry-level engineer who was sacked in June 2007, after working there for a year.
"His performance wasn't up to our standards, so we terminated him," Bernos said. There had been no contact between the company and Rodriguez since then.
After the shooting, scores of people left the building, with some telling the Associated Press that they had barricaded themselves inside their offices while the attack was taking place.
Will Halpern, an attorney working on the building's 17th floor, said that when he was evacuated he saw about about 20 officers in special weapons and tactics gear, carrying assault weapons, who were ready to search the building.
A main road through downtown Orlando was closed in both directions and schools close to the office block were locked down until the alleged gunman was caught.