Supporters of both Mr Mamboundou and Mr Obame gathered
Gabonese security forces have dispersed opposition supporters camped outside the electoral commission in the capital awaiting the results of Sunday's polls.
Earlier the electoral commission head told state television that a "misunderstanding" on how to verify the votes was delaying its announcement.
Three candidates, including the son of Gabon's long-time leader Omar Bongo, say they gained the most votes.
Ali Ben Bongo was pre-poll favourite to win the oil-rich nation's election.
Veteran opposition leader Pierre Mamboundou and former minister Andre Mba Obame have also claimed victory.
The BBC's Linel Kwatsi in the capital, Libreville, says huge crowds of opposition supporters - for both Mr Mamboundou and Mr Obame - gathered outside the commission building.
There is a heavy police presence in the capital ahead of the results
Witnesses told Reuters news agency that the security forces used tear gas to break them up.
Meanwhile, there is a party atmosphere at the headquarters of the ruling Gabonese Democratic Party (PDG), where officials think their candidate Ali Ben Bongo has been successful, our reporter says.
Security has been tightened across the capital as the nation awaits the results.
Sunday's vote was generally peaceful but tense, with long queues of voters waiting to chose a successor to Omar Bongo, who died in June.
One of the world's richest men, the late president owned a string of properties in France.
He was an unflinching ally of France and a key element in French influence in Central Africa. But he denied corruption charges in French courts.
BBC Africa analyst Martin Plaut says that Ali Ben Bongo is seen as less closely linked to the French elite than his father, despite being educated at the Sorbonne.
He is also somewhat detached from ordinary Gabonese, struggling to speak local languages with real fluency, he says.
Gabon is sub-Saharan Africa's fourth biggest oil producer and Africa's second biggest wood exporter, although most of its 1.4 million people live in poverty.