Fankhauser will meet with PM Mostafa Madbouly in Cairo after John and Susan Cooper fell ill last week and later died while staying at the Steigenberger Aqua Magic hotel in Hurghada.
The Egyptian authorities have said the couple died of natural causes, while Cook has said there was no evidence to suggest carbon monoxide poisoning was a factor.
The Coopers were holidaying with their daughter Kelly Ormerod, who was present when her parents fell ill and had maintained there was an unusual smell in the room the morning they fell fatally ill.
Cook has commissioned its own tests at the hotel covering food hygiene, water and air conditioning, although the results of these are not due until next week.
A Cook spokesperson said: “Thomas Cook chief executive Peter Fankhauser has flown to Egypt to meet with the Egyptian prime minister, His Excellency Dr Mostafa Madbouly.
"They will discuss the recent tragic deaths of Mr and Mrs Cooper in Hurghada and the ongoing investigation by the Egyptian authorities."
Following the deaths, Cook pulled all 301 of its guests out of the hotel citing a “raised level of illness”, offering them alternative accommodation or flights home.
Fankhauser, in the days following the tragedy, told various news outlets 13 people at the hotel had been suffering food poisoning, none of whom he said were in a serious condition.
Cook, it is understood, is yet to be granted access to the Coopers’ room at the hotel. Earlier this week, Fankhauser personally pledged “to get to the bottom” of the couple’s death.
John Cooper, 69, was taken ill last Tuesday morning (August 21) and died after his condition quickly deteriorated. His wife Susan, 63, a Thomas Cook agent in Burnley, passed away hours later.
Mrs Cooper’s colleagues paid touching tribute to their Chancery Walk colleague, describing her as the “life and soul” of the operator’s Burnley store.