Thomas Cook said its slow start to winter trading was also due to warm weather in Europe, following on from a weak finish to summer trading, when UK bookings fell 3% but prices rose 4.5%.
Thomson and First Choice parent TUI has responded to the crisis in Egypt by significantly shrinking capacity to the country and deploying most flights to other destinations, after countries including Germany advised holidaymakers not to travel there. Thomas Cook also said it is shifting capacity to match demand.
TUI said that while package holidays to Red Sea resorts remain on sale from the UK, demand has slumped.
TUI, Europe's biggest tour operator, reported a "strong" summer of UK trading, prompting it to hike full-year profit hopes. A 6% increase in prices and 2% more customers combined to lift its UK sales 8%, and most of its summer programme is now fully sold.
Excluding flights to Egypt, TUI said it has sold 29% of its UK winter programme, with bookings 4% ahead and average prices up 7%, resulting in sales up 11%.
Thomas Cook, which is midway through a painful turnaround driven by chief executive Harriet Green, said results for the year to the end of September will be in line with expectations despite the recent setback.
And Thomas Cook said that while it is at an early stage in the winter bookings cycle, average selling prices are up "strongly" in all markets.
It said: "Not unexpectedly, given geopolitical events and warm weather across Europe, winter trading has started more slowly than last year across most markets."
Across Europe, TUI said it has sold 31% of its mainstream winter programme and average selling prices across all markets with the exception of Egypt are up.
TUI said: "We remain confident in the flexibility and resilience of our business model which enables us to more effectively absorb the impacts of geopolitical events, including the current turbulent political situations in Egypt and Syria."
TUI said it now expects operating profit growth of 11% for the year to the end of September, up from its previous 10% guidance.