It was granted permission to land by Libyan authorities at the isolated World War II-era Kufrah airport in the southeast of the country after it ran short on fuel.
The passengers were reportedly given water but no food and some fainted when the air conditioning failed in the searing desert heat.
No movement has claimed public responsibility, but the director of Kufra airport said they belong to a faction of the Sudanese Liberation Army, whose exiled leader Abdel Wahid Mohammed Nur lives in Paris.
"The plane's pilot has indicated that the hijackers have said they belong to the Sudanese Liberation Army of Abdel Wahid Mohammed Nur," an official told Libya's official JANA news agency.
The plane's pilot said "the hijackers claim to have coordinated with him (Nur) to join him in Paris," he added.
"We condemned the hijacking and we have appealed to the international community to condemn it as well"
Ali Sadiq, Sudan's foreign ministry spokesman
But Nur, whose group was one of two movements that first rose up against the Arab-dominated Sudanese government in Darfur in 2003, denied any involvement.
"We categorically deny the responsibility of our movement in this hijacking operation," Nur told Al Jazeera in a telephone interview.
Bernard Kouchner, the French foreign minister, in Paris said that "everything is being considered" to protect the lives of those on board, while not saying explicitly whether France was prepared to receive the aircraft.
"If [Libyan leader] Colonel [Muammar] Gaddafi can convince the hijackers, and not harm the lives of the passengers, that's good, but otherwise everything must be done for the passengers' lives," Kouchner told Europe 1 radio.
Nur "is a true leader of a rebellion, of the resistance in Darfur, who says that he does not know these people and that he absolutely refuses to use these methods," Kouchner said.
Abdel Hafez Abdel Rahim, spokesman for Sudan's Civil Aviation Authority, said there were 95 people on the plane, including eight crew members and among the 87 passengers were two Egyptians and a Kenyan.
Sudan on Wednesday called on the Libyan authorities to arrest and deport to Khartoum the "terrorist" hijackers.
"We condemned the hijacking and we have appealed to the international community to condemn it as well," Ali Sadiq, spokesman for Sudan's foreign ministry, told Al Jazeera.
Speaking earlier to AFP news agency, Sadiq said consultations with the Libyans were aimed first at ensuring the safety and release of all Sudanese onboard, including the crew.
"Number two, to ensure that the hijackers be handed over to the government here to face the force of the law," Sadiq said.