The dawn raid came after Signatories in Blood, a jihadist group that claimed Thursday's blasts, threatened to continue attacking Niger until the country withdraws its forces from neighbouring Mali, where they are part of a French-led military campaign against Al-Qaeda-linked Islamists.
A French defence ministry official said two "terrorists" had been killed in the raid on a building at the Agadez army base, where Islamist fighters had holed up after the bombings and were holding a group of trainee soldiers hostage.
An elected official in Agadez, the main city in Niger's mostly desert north, gave a higher toll, saying three "terrorists" and three hostages had been killed, as well as a civilian caught in the cross-fire.
French Defence Minister Jean-Yves Le Drian confirmed France had taken part in the raid.
"The situation has stabilised as we speak, especially in Agadez, where our special forces intervened to back the Niger forces," he said on France's BFMTV.
Signatories in Blood, founded by veteran Algerian jihadist Mokhtar Belmokhtar, first grabbed worldwide attention in January when it seized an Algerian gas plant in a brazen attack that left 38 hostages dead.
Belmokhtar had been reported dead in April by Chad's President Idriss Deby Itno, who said the one-eyed extremist had been killed in fighting with Chadian troops in northeastern Mali.
But the jihadist group's spokesman El-Hassen Ould Khalil was quoted as saying by a Mauritanian news agency that "it was Belmokhtar himself who supervised the operational plans" in the Niger attacks.
The group also warned of "further operations" in Niger and threatened France and other countries involved in what it called the "Crusader campaign" in Mali.
Thursday's attack at the Agadez army base left 18 soldiers and one civilian dead, officials said. French nuclear group Areva said a near-simultaneous suicide bombing at its majority-owned uranium mine in northern Arlit had killed one and injured 14 employees.
Adding to the differing death toll figures in Agadez since Thursday's violence, Niger's Defence Minister Mahamadou Karidjo, speaking on public radio, said a total of 24 troops and eight Islamist assailants had died in the fighting.
Areva president and CEO Luc Oursel travelled to Niger on Friday to express his support for the victims and confirm the company's commitment to the country. "My visit here is a testament to the strength of our engagement in Niger," he said in a statement.
An Areva employee, who requested anonymity, said questions were still being asked as to how the attack could have happened considering "the impressive military and security apparatus" that was in place.
Meanwhile, Niger's public television network broadcast images of the destruction at the military base, including pieces of the suicide bombers' flesh strewn across the ground, debris from a four-by-four they blew up and roofs torn from buildings at the base.
Agadez residents said they were still reeling from the attacks, the first of their kind in the impoverished former French colony.
"People are still very shocked by what happened," Agadez tailor Babale Abdou told AFP by phone.
The UN Security Council on Friday "condemned in the strongest terms the terrorist attacks" and called for the perpetrators to be brought to justice.
Signatories in Blood was the second group to claim the attacks.
The Movement for Oneness and Jihad in West Africa (MUJAO), one of three Islamist groups that seized northern Mali last year before French-led troops drove them out, also claimed responsibility Thursday.
Signatories in Blood claimed the two groups had worked together and said Malian, Sudanese and Sahrawi or Western Saharan nationals had taken part.
MUJAO seized control of Mali's vast desert north in the chaotic aftermath of a March 2012 military coup together with allied groups Al-Qaeda in the Islamic Maghreb (AQIM) and Ansar Dine (Defenders of the Faith).
The groups ruled the region under a brutal form of Islamic law for 10 months until France sent in troops in January as the armed extremists advanced toward the southern capital, Bamako.
Belmokhtar was a top leader of AQIM before being forced out of the group late last year and launching his own attacks with Signatories in Blood.