The Niger military junta that seized power last week said on Monday the toppled government had authorised France to carry out strikes to try to free President Mohamed Bazoum.
The comments were made by army Col Amadou Abdramane, one of the coup plotters, on state television.
He said that the authorisation was signed by Niger Foreign Minister Hassoumi Massaoudou, acting as prime minister.
Mr Massaoudou could not be reached for comment.
The French Foreign Ministry did not confirm or deny the accusation but said Paris recognised only Mr Bazoum as a legitimate authority in the West African country and was focused on protecting its own citizens and interests there.
France, Niger's former colonial ruler, has condemned the coup and called for Mr Bazoum to be reinstated but has not announced any intention to intervene militarily.
The military junta, which seized power last week after blocking Mr Bazoum inside his presidential palace, has previously warned against foreign attempts to extract him, saying they would result in bloodshed and chaos. They named Gen Abdourahamane Tiani, the former presidential guard chief, as head of state.
Chadian President Mahamat Deby flew to Niger at the weekend to try to mediate, and early on Monday posted what appeared to be the first images of Mr Bazoum since the takeover, showing him smiling and apparently unharmed.
Mr Deby said he had met Mr Bazoum and coup leader Gen Tiani to explore ways “to find a peaceful solution”, without going into further detail.
African leaders on Sunday gave the junta in Niger one week to cede power or face the possible use of force, and imposed financial sanctions on the plotters.
At an emergency summit in Nigeria, the Economic Community of West African States regional bloc demanded Mr Bazoum be reinstated within a week.
Otherwise, the bloc said it would take “all measures” to restore constitutional order.
The military takeover in Niger, the latest coup in Africa's extremist-plagued Sahel region, has raised alarm on the continent and in the West. French and other foreign troops are stationed in Niger to help the army fight extremist militants.
The coup leaders said they overthrew Mr Bazoum due to poor governance and discontent with the way he handled the extremist threat.
The Kremlin said on Monday that the situation in Niger was “cause for serious concern” and called for a swift return to constitutional order.
Germany's Foreign Ministry said on Monday that the situation was still in flux and that there was a possibility the coup could fail.