Mr. Ping called for his supporters to “remain vigilant and mobilised”. There have been concerns about violent protests following the court ruling.
To ease tension Mr. Bongo offered to include opposition members in his cabinet.
He came to power in 2009 when his father died after ruling for 42 years.
President Bongo says he is now seeking to form a new government.
Speaking to supporters in the capital Libreville, Mr. Ping sought to ensure supporters that the Gabonese people would be “respected” and that “2016 will not be 2009″.
Mr. Ping had asked the court to re-examine results in the Haut-Ogooue province where Mr. Bongo won 95 per cent of the vote on a turnout of 99.9 per cent
But the court threw out copies of tally sheets that Mr. Ping had presented as evidence, saying they had not been verified.
Mr. Ping had warned that Gabon could face serious instability if the court rejected his appeal for a recount in that province.
Jean Ping appears to be in no mood to back down.
The opposition leader said the constitutional court was biased. But he’s not the only one to criticise the electoral process: the European Union says the Gabonese have the right to question the election’s integrity.
So far there has been no protests.
This time round the security forces have been very evident on the streets of the capital Libreville and elsewhere, and most people seem to be staying indoors.
In an interview with Reuters on Saturday Mr. Bongo called for political dialogue.
“I look forward to inviting members of all political parties to join our efforts and come with us to the cabinet.