Jean Ping, a former foreign minister who according to official results lost narrowly to Bongo in the August 27 vote, said Gabon had been the victim of a "military-electoral coup d'etat."
He called for "targeted sanctions against those responsible," including a freeze on assets held abroad and a ban on foreign travel.
Bongo was installed on Tuesday for his second term as president, three days after the Constitutional Court rejected Ping's demand for a recount.
His new prime minister, Emmanuel Ngondet, also tended an apparent olive branch today, saying negotiations were still under way for forming an "inclusive government" that would be unveiled on Sunday.
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But Ping, speaking at a press conference, angrily slapped down any notion of cooperation.
He reiterated he did not recognise Bongo as president, lashing him as "an imposter calling for dialogue."
"What dialogue?" he asked.
"This is someone who has been disavowed by the people and defeated at the ballot box, who is asking the person from whom he stole the election to come and dialogue with him... We won't go to any dialogue staged by this imposter."
A former French colony in central-western Africa, Gabon has vast assets in oil, minerals and timber, and has a per-capita national income that is far above the average for sub-Saharan Africa.
But a third of the population of 1.8 million still live below the poverty line, the result, say specialists, of chronic inequality and corruption.
Critics lay much of the blame at the door of the Bongo family, which has ruled the country for decades.
Ali Bongo, 57, took over from his father Omar Bongo, who ruled for 41 years until his death in 2009.
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