Know: Egypt Air hijacker 'frees all on board except four foreigners, crew'
The company had earlier tweeted that five foreigners and the crew remained on board, after negotiations with the hijacker who commandeered the domestic flight to Larnaca airport.
The identities of the foreigners was not immediately clear.
Cyprus police said the hijacker had contacted the control tower at 8:30 am (0530 GMT) and the plane was given permission to land at 8:50 am.
A crisis team was deployed to the airport, the main entry point for tourists to the Mediterranean resort island.
The plane was parked on the tarmac away from the new terminal building but just 200 metres (yards) from a beach where dozens of foreign tourists were out.
The aircraft was cordoned off by armed police.
The airport was closed during the crisis with incoming flights diverted to Paphos on the island’s western edge.
The hijacker made no immediate demands, Cypriot state television reported.
The EgyptAir plane was headed from the Mediterranean coastal city of Alexandria to Cairo with 81 passengers on board when it was seized, Egyptian civil aviation said.
The airline tweeted: “Our Flight MS181 is officially hijacked.”
The Cyprus foreign ministry confirmed in a statement that the flight “was hijacked and diverted to Larnaca international airport”.
It said “crisis management plans” had been put in place and that the country’s National Crisis Centre had been in contact with Egyptian authorities.
Cyprus government spokesman Nicos Christodoulides said on Twitter that President Nicos Anastasiades had spoken by telephone with Egyptian President Abdel Fattah al-Sisi.
The motive of the hijacking was not clear.
The incident came after a Russian airliner was downed on October 31 over the Sinai Peninsula, killing all 224 people on board. The Islamic State group claimed to have smuggled a bomb on board the plane.
Larnaca is no stranger to hostage crises. Several hijacked planes were diverted to the airport in the 1970s and 1980s.
In 1988, a Kuwait Airways flight hijacked en route from Bangkok to Kuwait was diverted to Mashhad and later to Larnaca, where hijackers killed two Kuwaiti passengers and dumped their bodies on the tarmac.
In February 1978, an Egyptian commando unit stormed a hijacked Cyprus Airways DC-8 at Larnaca airport, where 15 passengers were being held hostage. Some 15 Egyptian soldiers were killed and 15 wounded. All the hostages were freed and the hijackers arrested.