The head of the Algerian football federation, Mohammed Raouraoua, said his Egyptian counterpart, Samir Zaher, was to blame for the trouble.
"He is the origin of all the events that occurred, including the barbaric aggression that injured... our players," Mr Raouraoua said.
But Egyptian Foreign Minister Ahmed Abul Gheit has in turn told Algeria it must confront what he called the "saboteurs" who have attacked Egyptian businesses in Algiers.
Thousands of fans from both countries have already arrived in Khartoum for the play-off, arranged at a neutral venue by football's governing body Fifa after the teams could not be separated at the top of their group.
Sudanese officials say they are expecting 48 flights from Algeria and 18 from Egypt. A further 2,000 Egyptian fans are expected to travel by road.
Hotels in Khartoum are already booked out ahead of the game, and the authorities have set up two camp sites for rival fans several miles apart.
The stakes for each country are high. The last time either team was in the World Cup finals was 1990 for Egypt, and 1986 for Algeria.
There is a history of trouble between supporters of the two teams. Riots broke out in Egypt in 1989 after an Egyptian win in Cairo.
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