Official results from yesterday's vote are due out on Tuesday and candidates are prohibited by law from making such announcements.
"I have been elected. I am waiting for the outgoing president to call to congratulate me," veteran politician Ping, 73, said in the capital Libreville, prompting jubilation from hundreds of his supporters.
"Ping president!" they chanted.
"You have foiled the congenital fraud of this regime which we are finally going to see off," added Ping.
Bongo, 57, has been in power since a disputed election held in 2009 after the death of his father, Omar Bongo, who had ruled the oil-rich Central African country for 41 years.
Both of the two frontrunners had already predicted their own victory and accused the other of cheating.
Shortly after polling ended yesterday, the president's spokesman said: "Bongo will win... We are already on our way to a second mandate."
Interior Minister Pacome Moubelet Boubeya has said official results would be released around 1600 GMT on Tuesday and that it was "illegal to declare results before the relevant authorities do."
Earlier today, after Ping's camp had said it was well on the way to victory and that Bongo was trying to "trying to push his way through," with the backing of the army, the president's spokesman was dismissive.
The head of the Pan-African Democracy Observatory, an NGO based in Togo, played down the significance of Ping's declaration.
"We should not be surprised if one or the other declare victory. It's all part of the game," Djovi Gally told reporters.
Also today, the French embassy in Libreville warned its citizens not to travel within the country unless absolutely necessary for the time being and to keep themselves informed.
Today, the streets of Libreville were almost deserted.
Fearing a repeat of the violence that followed Bongo's victory in 2009, many residents, who had stocked up on food, stayed indoors.
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