However, the military has described it as "a pitiful sight" and a "relentless attempt to cling onto power". The internet and mobile-phone lines were cut a few hours after the coup announcement.
Authorities had earlier said five rebels had entered the building and four had been arrested.
His statement came hours after army Lieutenant Ondo Obiang Kelly read a statement on state TV saying young army officers were disappointed with a speech by President Ali Bongo on December 31 that he broadcast from Morocco, where he's been convalescing for two months after a stroke.
He also called for the formation of a Council of National Restoration and invited members of civil society and opposition parties, as well as a former Republican Guard commander to meet together at the country's parliament.
The Gabonese government said Monday it has quashed a coup attempt in the country.More news: Trade war ‘certainly’ hurting China economy, says USA official
In a message on state radio, military officers declared their dissatisfaction with Bongo, who is recovering from a stroke in Morocco.
Bongo is staying at a private residence in the Moroccan capital Rabat after suffering a stroke.
In the New Year's eve address, the president had sought to put an end to the rumours about his health, telling citizens that he was feeling fine.
"Once again, one time too many, the wielders of power deceptively continue to instrumentalise the person of Ali Bongo Ondimba, a patient devoid of many of his physical and mental faculties", said Obiang. But his words were slurred and he seemed unable to move his right arm.
Mr Bongo delivers a speech as he attends Heads of States' Statements ceremony of the COP21 World Climate Change Conference 2015.More news: Walton: Lakers needs 'more passion' from Ball, Ingram
Gabon, where the army Monday called for an uprising, is one of Africa's top oil producers and has been ruled for more than 50 years by the Bongo family.
President Bongo succeeded his father Omar Bongo as president in 2009.
US troops deployed to the central African nation of Gabon last week in response to potential violence in neighboring Democratic Republic of the Congo (DRC) remain committed to their mission despite prospective unrest linked to a failed coup attempt on Monday.
Bongo has only appeared in public twice since he was rushed to the hospital while attending an investment conference in Saudi Arabia on October 24.
Yields spiked to over 9 percent - level last seen on the 2024 bond in late November when oil prices hit their lowest level in over a year.More news: Boxer on the run after Paris riots