John Cooper, 69, and Susan Cooper, 63, from Burnley, Lancashire, died on Tuesday morning while on holiday at the resort with their daughter and her three children.
An inspection of the couple’s hotel room revealed there were no toxic or harmful gas emissions or leaks, a statement by Nabil Sadeq said.
His office is waiting for a forensic analysis of samples taken from the bodies, it added.
The couple’s deaths prompted tour operator Thomas Cook to evacuate all of its customers from the hotel as a “precautionary measure”.
The company said circumstances surrounding their deaths are “unclear” and that it received reports of “a raised level of illness among guests.”
Egyptian authorities dismissed criminal motives as being behind the deaths.
Medical examinations showed that the couple both fell ill after suffering “respiratory failure” while staying at the popular at the Steigenberger Aqua Magic Hotel.
The local governor’s office said the cause of Mr Cooper’s death was “a sudden stoppage of the heart muscles and respiratory failure”, with his wife dying due to “a stoppage of circulation and respiratory failure”.