Mr Putin has called for a return to constitutional order in Niger, while Wagner chief Yevgeny Prigozhin welcomed the coup.
The West African country has deepened its Soviet-era ties to Russia as its relationship soured this year with its long-time ally and former colonial ruler, France.
Amid mediation efforts by ECOWAS envoy Goodluck Jonathan, a Malian court on Friday declared coup leader Colonel Assimi Goita as president.
The country’s leadership has been hanging in the balance since the toppling of elected president, Ibrahim Kaita last August over corruption and incompetence in handling insurgency.