The standoff signals deep division within the army and a worrying new chapter for Burkina Faso, where a rampant Islamist insurgency has undermined faith in the authorities and displaced almost 2 million people, according to aid groups.
The West African country and former French protectorate has become the epicentre of violence carried out by groups linked to al Qaeda and Islamic State that began in neighbouring Mali in 2012 and has spread to other countries south of the Sahara Desert.
The Burkinabe army chief of staff called on opposing factions in a statement to cease hostilities and continue talks, adding that the situation was "an internal crisis within the National Armed Forces".
The U.S. State Department and the U.N. Secretary-General denounced the overthrow of the government.
"He strongly condemns any attempt to seize power by the force of arms and calls on all actors to refrain from violence and seek dialogue," a spokesperson for Antonio Guterres said in a statement.
Forces loyal to Traore appeared on state television and said Damiba had taken refuge in a French army base from where he was organising the counter-strike.
The French foreign ministry issued a statement saying the base had never hosted Damiba, who seized power in a Jan. 24 coup.
But hundreds of people who support Traore's takeover gathered in front of the French embassy in protest on Saturday. Anti-French demonstrators also gathered and stoned the French Cultural Centre in the Southern town of Bobo-Dioulasso.
In the early evening, a fire broke out at the embassy and several shots were heard. The embassy could not be reached for comment.
Earlier in the day, scattered shots rang out, armed helicopters circled the presidential palace and a convoy of special forces swept through central Ouagadougou after Traore announced on state television the previous evening that he had seized control in what would be the second coup this year.
"They led a counter-offensive this morning. Some of the special forces were sent ... and also the air base has been manipulated," Traore told radio station Omega on Saturday.
Damiba's whereabouts remain unknown.
Mali, Chad, and Guinea have all seen coups since 2020, raising fears of a backslide towards military rule in a region that had made democratic progress over the past decade.
(Additional reporting by David Lewis; Writing by Alessandra Prentice; Editing by Gareth Jones, Nick Macfie and Bate Felix)
By Thiam Ndiaga and Anne Mimault