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Sherif Fathy identified them as the pilot, the co-pilot, a female stewardess, a security officer and three passengers whose nationalities he refused to divulge.
He said negotiations with the hijacker - who had made no specific demands - were continuing, and that it was unclear whether the hijacker had taken explosives on board or whether he was bluffing.
An aircraft was being sent to Larnaca to pick up the passengers who had been released, Mr Fathy added.
Cypriot President Nicos Anastasiades said: "We are doing our utmost in order for everyone to be released and safe."
In response to a reporter's question about whether the hijacker was motivated by romance, he laughed and said: "Always there is a woman involved."
EgyptAir said the Airbus A320 was carrying 56 passengers from Alexandria to Cairo, along with six crew and a security official. It had earlier said 81 passengers were on board.
A statement from the Egyptian Civil Aviation Ministry statement said the 26 foreigners on board included eight Americans, four Britons, four Dutch citizens, two Belgians, two Greeks, a French national, an Italian, and a Syrian. Three other foreigners could not be identified.
"The pilot said that a passenger told him he had an explosives vest and forced the plane to land in Larnaca," the Egyptian civil aviation ministry said in a statement.
Larnaca airport, on the south coast of Cyprus, has been closed and scheduled flights diverted elsewhere.