Goïta says President Bah Ndaw and PM Moctar Ouane were trying to upend Mali's democratic transition after they took charge of an interim government last August that deposed President Ibrahim Boubacar Keita.
The two leaders were taken to a military base outside Bamako on Monday.
The UN, African Union and the European Union have condemned the move which has been described as an "attempted coup".
Al Jazeera's Nicolas Haque reports from Dakar, Senegal.
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