The Movement for Oneness and Jihad in West Africa (MUJAO claimed the near simultaneous bombings at the Agadez army base and a uranium mine in northern Arlit that is majority-owned by France's Areva company.
The movement added that the attack was done in retaliation for France’s military involvement in neighboring Mali.
Later a spokesman for Mokhtar Belmokhtar, who is the leader of a militant group in Maghreb, said the Algerian commander had "supervised" the suicide bombings in conjunction with MUJAO.
He said the near-simultaneous bombings "targeted elite French forces" who were providing security at the uranium mine in northern Arlit that is majority-owned by France's Areva.
The first car bomb went off at dawn Thursday at the army base in Agadez, the largest city in mostly desert northern Niger.
Eighteen soldiers and a civilian were killed along with four attackers at the army base, Interior Minister Abdou Labo said.
About 30 minutes after the first attack, a suicide bomber blew up a car at the Somair uranium mine and processing facility as employees reported for work at the site.
Areva said one person was killed at the mine located some 250 kilometres (150 miles) north of Agadez, but did not identify the victim. It added that 14 others were wounded.
A source at Areva in Niamey added that "the damage had forced the closure" of the uranium plant.
Somair is 64-percent owned by Areva and 36-percent owned by the state of Niger.