A Libyan official at the airport said the hijackers belonged to the Darfur rebel Sudan Liberation Movement led by Abdul-Wahid Nour.
But Yahia Bolad, a spokesman for the group, denied any involvement, saying his group had "no relation to this act".
The hijackers dismissed offers by Libyan authorities to provide the passengers with food and also rejected a request that passengers who had fainted because of inadequate air conditioning in the plane be given medical treatment, the Libyan news agency said.
The Sudanese passenger plane was reported to have nearly 100 people on board.
The Sun Air Boeing 737 was hijacked shortly after it took off from Nyala, the largest city in Sudan's Darfur region, on Tuesday, bound for Khartoum, airline officials said.
"After 20 minutes the pilot called Nyala airport to say the plane had been hijacked and that he is en route to Tripoli in Libya," one employee said.
A Sudanese government official told Al Jazeera that the hijacking was carried out by a "knife-wielding Sudanese man who threatened the pilot, and demanded that the plane be re-routed to Paris".
Libya's civil aviation authority later confirmed the plane had landed at the airport in remote Kufrah, an oasis town in the country's southeast.
The aircraft diverted to Libya after the authorities in Egypt refused permission for it to land in Cairo.