"The enemy was pushed back. According to preliminary data, two members of the National Guard were wounded and one attacker was killed," Bazoum said in a statement.
Early on Monday, one of the attackers blew himself up at the Koutoukale prison, situated about 30 miles from Niamey, the West African country's capital.
Niger has been a victim in the past of attacks from the Boko Haram group, which pledged allegiance to the Islamic State jihadist group, outlawed in Russia and many other states. The Niger army is part of a bloc that involves other military forces from Chad, Nigeria, Cameroon and Benin that is fighting the Boko Haram group in Nigeria and other neighboring countries.