Col Ibrahim Traoré also accused the French army of harbouring Lt Col Paul-Henri Damiba at one of its bases – but France denies any involvement.
Gunshots were heard in Burkina Faso’s capital city Ouagadougou on Saturday and helicopters have circled overhead.
Protesters started a fire outside the French embassy – an attack condemned “with the greatest firmness” by Paris.
The French foreign ministry told AFP news agency that the security of its compatriots was the greatest priority, adding that a crisis centre had been opened in Ouagadougou.
Earlier, witnesses said troops blocked main roads around the city and shops that had been open were later shut.
In the country’s second city, Bobo-Dioulasso, the gate of the French Institute was also reportedly set ablaze by protesters.
Friday’s apparent takeover had been announced on national TV and was the second time this year that the country’s army had seized power.
On both occasions the coup leaders said they had to step in because national security was so dire.
Burkina Faso controls as little as 60% of its territory, experts say, and Islamist violence is worsening. Since 2020 more than a million people have been displaced in the country due to the violence.
The African Union has demanded the return of constitutional order by July 2023 at the latest, agreeing with the regional group Ecowas that the ousting of leader Lt Col Damiba was “unconstitutional”.
Ecowas earlier said it was “inappropriate” for army rebels to seize power when the country was working towards civilian rule.
The latest international criticism has come from the UN, whose chief António Guterres says he “strongly condemns” the coup.
For the second time in under 24 hours the coup leaders have issued a statement on national TV, signed by their leader Col Ibrahim Traoré.
This time they claimed Lt Damiba was planning a counter-attack because of their own willingness to work with new partners in their fight against the Islamists. The statement did not name these potential new partners, but rights groups say troops in neighbouring Mali have been working closely with Russian mercenaries from the Wagner group – although both nations deny this.
On Friday evening flanked by rebel soldiers in fatigues and black facemasks, an officer had read an announcement on national TV stating that they were kicking out Lt Damiba, dissolving the government and suspending the constitution.
That statement was also read on behalf of an army captain called Col Traoré, who said Lt Col Damiba’s inability to deal with an Islamist insurgency was to blame.
“Our people have suffered enough, and are still suffering”, he said.
Little is known about Col Traoré, the 34-year-old soldier who led an anti-jihadist unit in the north called Cobra.
His statement effectively declared himself the interim leader of Burkina Faso. But in Friday’s announcement came the promise that the “driving forces of the nation” would in time be brought together to appoint a new civilian or military president and a new “transitional charter”.
Lt Col Damiba’s junta overthrew an elected government in January citing a failure to halt Islamist attacks, and he himself told citizens “we have more than what it takes to win this war.”
But his administration has also not been able to quell the jihadist violence. Analysts told the BBC recently that Islamist insurgents were encroaching on territory, and military leaders had failed in their attempts to bring the military under a single unit of command.
On Monday, 11 soldiers were killed when they were escorting a convoy of civilian vehicles in Djibo in the north of the country.
The African Union has urged the military to “immediately and totally refrain from any acts of violence or threats to the civilian population, civil liberties, human rights”.
The Economic Community of West African States (Ecowas) earlier condemned the move too, stating it “reaffirms its unreserved opposition to any taking or maintaining of the power by unconstitutional means”.
The United States said it was “deeply concerned” by events in Burkina Faso and encouraged its citizens to limit movements in the country. France issued a similar warning to its more than 4,000 citizens living in the capital city Ouagadougou.
“We call for a return to calm and restraint by all actors,” a US State Department spokesperson said.
In January, Lt Col Damiba ousted President Roch Kaboré, saying that he had failed to deal with growing militant Islamist violence.
But many citizens do not feel any safer and there have been protests in different parts of the country this week.
On Friday afternoon, some protesters took to the capital’s streets calling for the removal of Lt Col Damiba.
The Islamist insurgency broke out in Burkina Faso in 2015, leaving thousands dead and forcing an estimated two million people from their homes.
The country has experienced eight successful coups since independence in 1960.