Algerian militant Mokhtar Belmokhtar is reported to have masterminded the two suicide bombings in Niger on Thursday.
A Signed-in-Blood Battalion spokesman told Mauritanian news agency Alakhbar that he had "supervised" the attacks, carried out with another group, Mujao.
The bombers targeted a military base in Agadez and the French-run uranium mine in Arlit, killing 21 people.
On Friday, French special forces and Nigerien troops shot dead two militants holed up inside the base at Agadez.
Niger's Defence Minister, Kardijo Mahamadou, said they had barricaded themselves inside a dormitory along with two soldiers, who were freed during the operation.
"Our military forces and French special forces assaulted [the building] and the hostages - a total of two people - were freed," he told the Associated Press. "There were two kidnappers who were hiding in the military dorm, and both were killed. The operation is now finished."
Mr Mahamadou separately told RFI radio that eight Islamist militants had been killed in the Agadez operation and two others in Arlit, adding: "All of them were wearing belts packed with explosives."
France's Defence Minister, Jean-Yves Le Drian, told BFM television that its troops had intervened at the request of Nigerien President Mahamadou Issoufou and that the situation had "stabilised".
A French defence ministry official also told AP that the two soldiers held hostage by the militants had been freed in the assault. Earlier, local and military sources told the BBC that they had been killed.
Thursday's bombing at the barracks in Agadez killed 19 people, including 18 soldiers. Four attackers also died while a fifth was overpowered by security forces.
The attack on the Somair mine, in the town of Arlit, killed one person and injured 14 others, its operator Areva said.
Alakhbar quoted El-Hassen Ould Khalil, a spokesman for al-Muwaqqioun bi-Dima (Signed-in-Blood Battalion), as saying: "It was Belmokhtar who himself supervised the operational plans of attacks."
The attacks "targeted elite French forces" who were providing security at the uranium mine that is majority-owned by Areva, he added.
An online statement, reportedly signed by Mokhtar Belmokhtar, read: "This is the first of our responses to the statement of the president of Niger - from his masters in Paris - that he eliminated jihad and the mujahideen militarily."
Earlier, the Movement for Unity and Jihad in West Africa (Mujao) also said it had carried out the two attacks. However, Mr Khalil's statement to Alakhbar said the Signed-in-Blood Battalion had jointly led the attacks with Mujao.
Mujao spokesman Abu Walid Sahraoui said on Thursday that its militants had targeted "the enemies of Islam in Niger", according to the AFP news agency.
"We attacked France, and Niger because of its co-operation with France, in the war against Sharia [Islamic law]," he added, thought to be a reference to French and Nigerien involvement in driving out Mujao and two other Islamist groups from northern Mali earlier this year.
In the statement threatening further attacks, Mokhtar Belmokhtar's group warned against Western intervention in the region.
"Columns of commandos and those seeking martyrdom are ready and waiting for their targets," it said.
"We will have more operations, by the strength and power of Allah, and not only that, but we will move the battle to the inside of his country if he (the president of Niger) doesn't withdraw his mercenary army," another statement to Mauritania's ANI news agency said.
On Thursday, French President Francois Hollande vowed to protect French interests and co-operate with Niger in its "fight against terrorism".
Mokhtar Belmokhtar was believed to be behind the deadly attack on an internationally run Algerian gas plant in January in which 37 hostages and 29 insurgents were killed.
He broke away from al-Qaeda in the Islamic Maghreb (AQIM) last year and formed a new jihadist group, known variously as the Signed-in-Blood Battalion, the Masked Men Brigade and the Khaled Abu al-Abbas Brigade.
Armed forces in Chad said he died in a raid in northern Mali on 2 March, although there was no confirmation and his death has been declared many times before.
Mujao (the Movement for Unity and Jihad in West Africa) is a splinter group of AQIM which operates mostly in northern Mali.
It says its objective is to spread jihad to West Africa rather than confine itself to the Sahel and Maghreb regions - the main focus of AQIM.