Traore's team urged people to refrain from acts of vandalism at the embassy, targeted by protesters after an officer involved in the ongoing coup said France had sheltered President Paul-Henri Damiba at a French military base in the West African country and that he was planning a counter-offensive.
The French foreign ministry denied the base had hosted Damiba after his ouster on Friday. Damiba also denied he was at the base, saying the reports were a deliberate manipulation of public opinion. His whereabouts remain unknown.
"We want to inform the population that the situation is under control and order is being restored," an army officer said in a statement broadcast on national television. Traore, an army captain, stood beside the officer and was flanked by other armed and masked soldiers.
The city was mostly calm on Sunday after sporadic gunfire across the capital throughout Saturday between opposing factions of the army.
"We invite you to continue with your activities and refrain from all acts of violence and vandalism... notably that against the French embassy and the French military base," the officer loyal to Traore said, urging people to remain calm.
Damiba himself led a coup earlier this year against a civilian government that had lost support over rising violence by Islamist extremists. Damiba's failure to stop attacks by the militant groups had led to anger in the ranks of the armed forces in the former French-protectorate.
The statement came after hundreds of people, some waving Russian flags and supporting Traore's takeover gathered in protest in front of the French embassy on Saturday and Sunday, throwing stones and burning tires and debris on Saturday and early on Sunday.
Anti-French demonstrators also gathered and stoned the French Cultural Centre in the Southern town of Bobo-Dioulasso. French business interests were also vandalised on Sunday morning.
Burkina Faso has become the epicentre of attacks carried out by groups linked to al Qaeda and Islamic State, after violence that began in neighbouring Mali in 2012 spread to other countries south of the Sahara Desert.
Thousands have been killed in raids on rural communities and millions have been forced to flee despite Damiba's promise to tackle insecurity following his coup in January. This week, at least 11 soldiers died in an attack in northern Burkina Faso. Dozens of civilians are still missing following the attack.
(Reporting by Thiam Ndiaga and Anne Mimault Writing by Bate Felix; Editing by Kirsten Donovan and Frank Jack Daniel)
By Thiam Ndiaga and Anne Mimault