But Thomas Cook said the circumstances around their deaths were still unclear, when ruling out the poisonous gas as a possible factor.
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.
Thomas Cook said Thursday it had received reports of "a raised level of illness" among some of its other 300 customers at the Steigenberger.
"Safety is always our first priority, so as a precautionary measure we have taken a decision to remove all our customers from this hotel", the company said.
But by Friday evening, about half the 301 guests had been flown out of Egypt, and the remainder had moved to nearby resorts, a Thomas Cook spokeswoman said.
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Thomas Cook audited the Steigenberger Aqua Magic in July, 2018 and received an overall score of 96 per cent.
The BBC said there were a total of 1,600 guests at the hotel.
The office spokesperson continued: "There was no reason to suspect the death was of a criminal nature".
She added the family were in "utter shock" as they await results of post-mortem examinations on the couple, who had booked the holiday with Thomas Cook.
Carol Mackenzie, Thomas Cook's head of customer welfare, told Sky News she flew out to provide support to the family affected by the deaths.
"I subsequently have been ill for several weeks now since returning and had to visit the doctors on two occasions with two full weeks of antibiotics", she said.
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Egyptian officials are insisting that a British couple both died of heart failure at a hotel in the north African country, as their daughter demands answers over why. His wife was taken to a hospital where she also died.
He said he thinks it could be either carbon monoxide poisoning, food poisoning or water poisoning.
The "circumstances" of their deaths "are still unclear", it added.
An Egyptian official told The Associated Press that an investigation was still underway but that the deaths were likely due to "natural causes". "There are no indications to support allegations of an increased incidence of illness at the hotel".
The Foreign Office said in a statement: "We are supporting the family of a British couple who died in Hurghada, Egypt and we are in contact with the local tour operator".
After the bombing of a Russian passenger jet flying from Sharm el-Sheikh in the Sinai Peninsula in 2015, Egypt-bound flights from Russia were halted for more than two years, hurting Egyptian tourism revenues.
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