The refusal by Ping, who says he won the presidential poll, to accept the court ruling raises the prospect of a potentially violent political crisis in the central African oil producer.
Opposition leader rejects court ruling upholding Ali Bongo poll win
Speaking to supporters and reporters at his residence in the capital Libreville, Ping called for people to "remain vigilant and mobilised".
Recommended articles
The court had agreed to Ping's petition to re-examine results in Haut-Ogooue province, where Bongo was declared to have won 95 percent on a turnout of 99.9 percent.
However, in a ruling late on Friday, it refused to accept copies of vote tally sheets provided as evidence by Ping, stating he had failed to prove their authenticity.
"We will ensure the choice of the Gabonese people is respected. 2016 will not be 2009," Ping said.
Ali Bongo came to power in a contentious 2009 election following the death of his father Omar Bongo, who was president of Gabon for 42 years.
Ping, a lifelong political insider in Gabon who has also served as chairman of the African Union Commission, was a close ally of Omar Bongo.
President Ali Bongo sought to ease tensions on Saturday, calling for dialogue and promising a new inclusive government.
"I look forward to inviting members of all political parties to join our efforts and come with us to the cabinet," he told Reuters in an interview.
He said the new government would "most likely" include leading opposition figures and did not rule out the possibility of reserving a place for Ping.
However, he rejected the option of international mediation.
"We don't need international mediation. Among Gabonese, we know how to talk to each other," he said.
JOIN OUR PULSE COMMUNITY!
Eyewitness? Submit your stories now via social or:
Email: eyewitness@pulse.ng