Before Bazoum's legal representatives released their statement, Niger's junta said the deposed leader was being "held incommunicado."
Mohamed Seydou Diagne, the coordinator of a lawyers' collective, released a statement that said, "We strongly reject these fabricated accusations against President Bazoum."
Holding Bazoum "incommunicado," the lawyer added, was "a new red line which has been crossed by a junta which continues to violate the fundamental rights of our client."
Late Thursday, the military commanders who overthrew the democratically elected Bazoum on July 26 said they had foiled an attempt by him early in the day to escape their custody.
In a televised address, Amadou Abdramane, the spokesperson for Niger's junta said, "at around three in the morning, the ousted President Mohamed Bazoum and his family, his two cooks and two security elements, tried to escape from his place of detention."
The alleged escape bid failed and "the main actors and some of the accomplices" were arrested, he added.
Abdramane said the escape plan had involved Bazoum first getting to a hideout on the outskirts of the capital Niamey.
They had then planned to fly out on helicopters "belonging to a foreign power" toward Nigeria, he added.
Since he was toppled, Bazoum has refused to resign and had been held at his residence in the heart of the presidential palace along with his wife Haziza and son Salem.
The military has not said where he is being held now.