A surviving attacker took a group of soldiers hostage, and authorities were attempting to negotiate their release.
The timing of the attacks, which occurred at the same moment more than 100 miles apart, and the fact that the bombers were able to penetrate both a well-guarded military installation and a sensitive, foreign-operated uranium mine, highlight the growing reach and sophistication of the Islamist extremists based in neighboring Mali.
Both attacks were claimed by a spinoff of al-Qaeda's local chapter, the Movement for Oneness and Jihad in West Africa, or MUJAO, said French radio RFI.
The highest toll was in the desert city of Agadez, located almost 1,000-km northeast of the capital, where the attackers punched their explosive-laden car past the defences at a military garrison and detonated inside the base, killing 20 soldiers and 16 others, said Niger's Minister of Defence Mahamadou Karidjo.
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Three suicide bombers also died, but a fourth escaped and grabbed a group of military cadets, added Interior Minister Abdou Labo.
Over 240-km northeast of Agadez, a different group of two suicide bombers slipped past a truck to enter a uranium mine operated by French nuclear giant Areva, injuring 14 employees of the French company, one of whom died later. Both suicide bombers were also killed, according to sources.
France had scrambled war planes over Mali and sent in forces to try take back the country's al-Qaeda-held north, prompting the extremists to swear revenge.
The military of Niger had sent 650 troops to help France combat the Islamists in Mali.
The government of Niger has decreed a 72-hour period of national mourning following the heavy toll from the latest attack.