Niger's junta denounced the comments as divisive and served only to perpetrate France's neo-colonial relationship.
Gabon's coup is only the latest in countries throughout Africa's Sahel region.
The deterioration in Niger-France relations echoes post-coup developments in Mali and Burkina Faso, which have booted out French forces and severed long-standing ties.
Perceived-Western backing of state actors could create future divisions in an already tense climate.
Niger is one of the least prosperous countries in the world, but has critical strategic value for several reasons.
The borders that have reopened are mainly in remote desert areas. Niger's key entryways for trade and commerce remain closed due to sanctions imposed by the regional bloc.
"Any military intervention against Niger would be considered as a declaration of war against Burkina Faso and Mali," a statement reads.
There have been at least seven other coups and military takeovers in Africa in the last decade.
"The President of the CNSP is the head of state. He represents the state of Niger in international relations," an officer said, reading out a statement.
"What happened in Niger is nothing other than the struggle of the people of Niger with their colonizers," Prigozhin said.