The head of the Russian mercenary Wagner group, Yevgeny Prigozhin, has welcomed the takeover in Burkina Faso.
Meanwhile, the Russian government said on Monday it “would like the situation in Burkina Faso to normalise as soon possible”.
Burkina Faso controls as little as 60% of its territory, experts say, and Islamist violence is worsening.
The African Union has demanded the return of constitutional order by July 2023 at the latest, agreeing with the regional group Economic Community of West African States (Ecowas) that the ousting of leader Lt Col Damiba was “unconstitutional”.
But Ecowas has since praised “the various parties in Burkina Faso for agreeing to a peaceful settlement of their differences”, as days of power struggles came to an end without bloodshed.
It is still not clear where Burkina Faso’s ousted leader is, and no statement has been released by him directly.
But religious and community leaders on Sunday said Lt Col Damiba himself had offered his resignation “in order to avoid confrontations with serious human and material consequences,” according to quotes cited by AFP news agency.
They said Lt Col Damiba had set seven conditions for stepping down – including a guarantee of his security, an agreement to continue with efforts at national reconciliation and a continued respect for the guarantee of returning to civilian rule within two years.
The deposed colonel had himself ousted President Roch Kaboré in January, saying that he had failed to deal with growing militant Islamist violence.
Many citizens in Burkina Faso have not felt safe for some time.
The Islamist insurgency broke out in the country in 2015, leaving thousands dead and forcing an estimated two million people from their homes.
This is Burkina Faso’s ninth coup since independence from France in 1960.