Also announced on the Internet site of French weekly newspaper Le Point, Bongo's death was not officially confirmed by either Gabon or France's foreign ministry.
"I was very surprised, like many of my compatriots, to learn of the death of of the Gabonese president via French television," Gabon Prime Minister Jean Eyeghe Ndong said in Libreville. "There are procedures: to begin with, the president has a family."
Bongo, who led the former French colony in west Africa since 1967, had officially been in a clinic in Barcelona, Spain for a medical check-up but several sources said he was being treated for advanced cancer.
"He was a great figure of Africa," a "man who had influence," said French Defence Minister Herve Morin when told of his death.
Bongo came to power with French support and ruled over a state that grew rich on its abundant oil while most of the 1.5 million population remain impoverished.
His last months were marked by a row with Paris over a French inquiry into luxury properties he had bought in the country and claims by anti-corruption activists that they were acquired with embezzled state funds.
A French court decision in February to freeze Bongo's bank accounts added fuel to the fire and his government accused France of waging a "campaign to destabilise" the country.
The assets freeze was part of a probe to find out if Bongo, his ally President Denis Sassou Nguesso of Congo-Brazzaville and Equatorial Guinea's President Teodoro Obiang Nguema had plundered state coffers.
The leaders denied any wrongdoing.
Gabon had also been angered by French media coverage of the hospitalisation of its president, accusing French broadcasters of reporting "non-official and alarmist" information on his condition.
Bongo announced on Friday that he was temporarily suspending his duties in order to rest and mourn the death in March of his 45-year-old wife Edith Lucie Bongo Ondimba.
His wife, who was the daughter of Congo President Nguesso, died in Morocco in March after a long illness.
Gabon was the first African country to host French oil giant Elf in the 1960s, from where it operated as a state within a state, serving as a base for French military and espionage activities.
The Paris trial in 2003 of former Elf chairman Loik Le Floch-Prigent revealed the extent of the corruption and shady dealings in Gabon's booming oil business under Bongo.
"Gabon without France is like a car with no driver. France without Gabon is a like a car with no fuel," is how Bongo described the relationship between France and its former colony.
But relations deteriorated due to the French court decision to probe Bongo's Paris properties.
President Nicolas Sarkozy's government is also considering dismantling its 1,000-strong army base in Libreville as part of a broad shake-up of its military presence in Africa.
Bongo opted to seek medical care in Spain instead of Paris, where his predecessor Leon M'Ba died in 1967.
Favourite to succede him is his 50-year-old son Ali Ben Bongo, although observers said nothing was for certain after such a long rule and in a country with many ethnic groups to satisfy.
Ali Ben Bongo, a former Gabonese foreign minister, was reshuffled to head the crucial defence ministry in 1999 by his father to snuff out any would-be coup but also with his succession in mind.