The AU's Peace and Security Council said all member states and the international community should "refrain from any action that could legitimise Niger's junta", which seized power last month.
It also noted a decision by the West African Ecowas bloc to activate a standby force for possible military intervention and asked the AU Commission to assess the economic, social and security implications of deploying such a force.
Niger has been largely isolated internationally after Presidential Guard Commander Abdourahmane Tchiani confined Mr Bazoum and his family to house arrest and declared himself leader.
In response, France and several other western states which have forces in Niger to fight extremist groups in the Sahel, promptly evacuated their citizens and cut off aid to the impoverished nation, which has since had sanctions imposed by Ecowas.
The coup on July 26 is the seventh in West and Central Africa in three years.
Military rulers in Mali, Burkina Faso and Guinea have supported the junta, saying an Ecowas military deployment would be regarded as a "declaration of war" in their own countries.
Ecowas said its members have agreed on an undisclosed "D-Day" for a possible military intervention if diplomatic efforts fail.
Algeria rejected a French request to fly over its airspace for a military operation in Niger, state radio said late on Monday.
Algeria opposes any foreign military action in Niger and favours diplomacy to restore constitutional order, it added.
President Abdelmadjid Tebboune voiced Algerian fears about an armed response early this month, saying "a military intervention could ignite the whole Sahel region and Algeria will not use force with its neighbours".