Bongo claimed victory in the August 27 poll by a wafer-thin margin of some 6,000 votes.
But a European Union delegation deployed in Gabon to monitor the vote said there was a flaw in voting in Haut-Ogooue province, the incumbent's fiefdom.
"An analysis of the number of non-voters as well as blank and disqualified votes reveals a clear anomaly in the final results in Haut-Ogooue," the observers said in a statement.
Even after the vote result in the other provinces had been settled, electoral commission members fiercely debated the count for Haut-Ogooue, the heartland of Bongo's Teke ethnic group, before the incumbent was declared the winner on Wednesday.
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"There needs to be a clear electoral process," French Prime Minister Manuel Valls told radio station RTL on today, saying there were "some doubts".
"It would be wise to do a recount."
France, the EU and the United States had already called for the results to be published according to each polling station, but until now had stopped short of demanding a recount.
Bongo's defeated rival Jean Ping, a veteran diplomat who has held a top African Union job, yesterday called for a general strike to oust "the tyrant."
But his appeal appeared to go largely unheeded in the capital Libreville today like the previous day when banks and shops re-opened after being shuttered due to post-election violence.
Communications minister and government spokesman Alain-Claude Bilie-By-Nze called demands for a recount a "plot" and accused foreigners of trying to manipulate the results.
According to an AFP count, post-election chaos has claimed at least seven lives in the oil-rich central African nation, ruled by the Bongo family since 1967.
Gabonese authorities, however, said yesterday the toll was three killed and 105 wounded, with the government saying some deaths had previously been incorrectly attributed to the clashes.