The country's foreign minister Hassoumi Massoudou also issued a rallying cry on X, the platform formerly known as Twitter, for "all democrats and patriots" to make the coup fail.
Their statements on Thursday followed a late-night address on Wednesday by soldiers on national television announcing Bazoum had been removed from power and all institutions of the republic suspended, marking the seventh coup in West and Central Africa since 2020.
Earlier on Wednesday, members of the presidential guard had cut off the presidential palace in the capital Niamey and blocked Bazoum inside, sparking regional and international concern about instability in a country that is a pivotal ally for Western powers helping fight an insurgency in the Sahel region.
Bazoum was still being held inside the presidential palace on Thursday morning, Massoudou said in an interview with French broadcaster France 24.
The minister's whereabouts were unclear.
Niamey was quiet on Thursday morning as citizens awoke to closed borders and a nationwide curfew imposed by the military.
Several Bazoum supporters had gathered in the city as events were unfolding on Wednesday, voicing their opposition to a change of power, a Reuters reporter said.
They were later dispersed.
It is not yet clear who has taken command.
The presidential guard is headed by General Omar Tchiani, but the televised statement was read by a member of the air force named Colonel Amadou Abdramane.
Seated in an office rather than in the television studio and flanked by nine other officers in fatigues, Abdramane said defence and security forces had acted in response to deteriorating security and bad governance.
Land-locked Niger, a former French colony, is one of several West African states battling jihadist militants who have waged a violent insurgency across the region in the past decade.
Frustrations over state failures to prevent violent attacks on towns and villages partly spurred two coups in Mali and two in Burkina Faso since 2020.
Niger's role had become increasingly important for Western powers helping fight the jihadists since relations with Burkina Faso and Mali's military governments soured, prompting foreign troop withdrawals.
Niger is also a key ally of the European Union in the fight against irregular migration from sub-Saharan Africa.
France moved troops to Niger from Mali last year after its relations with interim authorities there soured.
It has also withdrawn special forces from Burkina Faso amid similar tensions.
Bazoum's election was the first democratic transition of power in a state that has witnessed four military coups since independence from France in 1960.
The United States says it has spent about $US500 million ($A739 million) since 2012 to help Niger boost its security.
Ulf Laessing, head of the Sahel program for Germany's Konrad-Adenauer-Stiftung think-tank, said a coup would create an opportunity for Russia and other actors to spread their influence in Niger.
The US has urged Bazoum's release, while the EU, United Nations, France and others condemned the uprising and said they were following the events with concern.
US Secretary of State Antony Blinken, who spoke with Bazoum when he was being held in the presidential palace, said the US economic and security partnership with Niger depended on the continuation of democratic governance.
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