It comes shortly after the US declared its "unflagging support" for ousted president Mohamed Bazoum - seen as a key Western ally in the fight against Islamist militants.
On Friday the head of the presidential guards unit Gen Abdourahmane Tchiani declared himself Niger's new leader.
He said insecurity, economic woes and corruption led him to seize power.
But there are now concerns in the West about which countries the new leader will align with.
Niger's neighbours, Burkina Faso and Mali, have both pivoted towards Russia since their own coups.
EU foreign policy chief Josep Borrell joined the US and France in refusing to recognise the coup leaders and said security cooperation and budgetary aid was being suspended indefinitely.
Also on Saturday France, the former colonial power which had moved its regional military headquarters to the country after being forced to leave Mali, said it had suspended all development aid and budgetary support.
Meanwhile the African Union called on the Niger army to return to base within 15 days.
On Friday evening US Secretary of State Antony Blinken warned those detaining Mr Bazoum - Niger's first elected leader to succeed another since independence in 1960 - that "hundreds of millions of dollars of assistance" was at risk.
However, the leader of Russia's Wagner mercenary group has reportedly described the coup as a triumph.
"What happened in Niger is nothing other than the struggle of the people of Niger with their colonisers," Yevgeny Prigozhin was quoted as saying on a Wagner-affiliated Telegram channel.
"With colonisers who are trying to foist their rules of life on them and their conditions and keep them in the state that Africa was in hundreds of years ago."
He added: "Today this is effectively gaining their independence."
The BBC has not been able to verify the authenticity of his reported comments.
Wagner is believed to have thousands of fighters in countries including the Central African Republic (CAR) and Mali, where it has lucrative business interests but also bolsters Russia's diplomatic and economic relations.
