The landlocked nation is the fourth member of the Economic Community of West African States (ECOWAS) hit by a putsch since 2020.
ECOWAS has threatened potential use of force if the military in Niger does not restore ousted President Mohamed Bazoum by Sunday, and military chiefs of the bloc's member countries met in Nigeria on Wednesday for three days of consultations.
"Any aggression or attempted aggression against the State of Niger will see an immediate and unannounced response from the Niger Defense and Security Forces on one of [the bloc's] members, with the exception of suspended friendly countries," one of the rebels said in a statement read on national television, alluding to neighboring Burkina Faso and Mali.
ECOWAS has already imposed trade and financial sanctions after the coup.
The military leadership also announced Thursday it was ending the mandates of its ambassadors to four countries, as well as scrapping military pacts made between Niamey and France.
"The functions of the extraordinary and plenipotentiary ambassadors of the Republic of Niger" to France, Nigeria, Togo and the United States "are terminated," it said.
Blaming France's "careless attitude and its reaction to the situation," it said it had "decided to scrap the cooperation agreements in the field of security and defense with this state".
Niger has had a key role in Western strategies to combat the jihadist insurgency that has plagued the Sahel since 2012, with France and the United States stationing around 1,500 and 1,000 troops in the country, respectively.
On July 26, Niger's presidential guard removed President Mohamed Bazoum from power. The guard's commander, Gen. Abdourahmane Tchiani, proclaimed himself the country's new leader.