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Mursi had been due to arrive in Paris on Thursday afternoon following a visit to Berlin on Wednesday and later meet Hollande over breakfast on Friday.
Mursi's spokesman Yasser Ali said in Cairo that the president would reschedule a visit at another time.
When pressed to give a reason, he said: "The president will travel to Germany on a one-day trip and return to Egypt to closely follow the situation."
Mursi declared a month-long state of emergency on Monday in three cities on the Suez Canal in the face of violent anti-government protests.