The Algerian side celebrate World Cup qualification
Egypt has threatened to quit football for two years after complaining to Fifa over the behaviour of Algerian fans.
Algeria won a play-off to progress to the World Cup after the teams finished joint top in their qualifying group.
Egypt are being investigated after reports that Algeria's bus was pelted, while Egypt claims fans and players were threatened before a later match.
"We will stop playing for two years in protest at what happened during the attack," an Egyptian statement said.
Referring to the later match, the statement by Egypt's Football Federation added: "Egyptian fans, officials and players put their lives at risk before and after the game, under threat from weapons, knives, swords and flares.
"We have stated most seriously in the complaint to Fifa to restore moral discipline to the world of football.
"We are ever confident and know that Fifa has always sought to preserve the lives of players and fans, and stand firmly against anyone who tries to distort the ethics and principles of world football.
"A meeting will be held between the head of the National Council for Sport and the president and vice-president of the Egyptian Federation."
Fifa is currently investigating the Egyptian FA after reports that Algerian players were attacked in Cairo before the first of the matches.
Egypt won that game 2-0, forcing a play-off in neutral Sudan to decide which team would qualify for the World Cup.
But Algeria were 1-0 winners of Wednesday's play-off game at the Khartoum Stadium.
World Cup footballers under attack
It had been reported that Egyptian fans pelted the Algerian team's bus with stones, injuring three players, and that some fans were hurt in scuffles before the Cairo qualifier.
"Disciplinary proceedings have been opened against the Egyptian Football Association," Fifa said in an earlier statement.
"According to the official reports received by Fifa, on November 12 there were incidents affecting the Algerian team on their way from the airport to the hotel."
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