"I pledge to devote all my efforts for the good of the Gabonese people and to ensure their well-being... And respect and defend the constitution and the rule of law," the 57-year-old said.
Cannons were fired during the ceremony in the seafront presidential palace in Libreville, as fears of fresh violence resurfaced.
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Government spokesman Alain-Claude Bilie-By-Nze said Bongo wanted to install "a unity government by this week or the start of next week".
Bongo's second mandate has received a cool reception from the African Union and the United Nations, while the European Union voiced regret that the count had not been transparent.
The Gabonese spokesman was dismissive of former colonial ruler France, which sent its ambassador to the event.
"Whether they come or not doesn't change anything. France has no diplomacy any more. It's getting its orders from Brussels," he said.
Bongo's wafer-thin victory in the August 27 vote was confirmed on Saturday by the country's top court, which dismissed opposition claims of vote fraud.
Ping, 73, who came second in the vote, lashed the court's ruling as a miscarriage of justice and declared himself "president elect".
He has so far not responded to Bongo's overtures for a dialogue.
A career diplomat and a former top official at the African Union, Ping had filed a legal challenge after Bongo was declared the winner by a mere 6,000 votes.
Violence initially erupted on August 31 after Bongo was first declared the winner. Demonstrators set parliament ablaze and clashed with police, who made a thousand arrests.
Opposition figures say more than 50 people were killed. The government has given a toll of three dead.
Ping had asked for a recount in Haut-Ogooue province, where 95 per cent of voters in the Bongo family stronghold were reported to have cast their ballots for the president on a turnout of more than 99 per cent.
In its final tally, the court ruled Bongo had won 50.66 per cent of the vote (172,990 votes) and Ping 47.24 per cent (161,287 votes).
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