The violence prompted President Mahamadou Issoufou to cut short a trip to Egypt.
Unrest over deadly ambushes has mounted, particularly in Mali, where soldiers' widows have held a number of demonstrations calling on the government to do more.
US jobless claims hit 2-year high
The number of people already collecting unemployment benefits beyond the initial week fell by 31,000 to 1.67 million. Jobless claims rose by 49,000 to 252,000 in the week ended December 7, Labor Department data showed Thursday.
Two of the sources said another 30 soldiers had been wounded and that the military base had been taken over by the assailants.
Four U.S. service members were killed, along with four Nigerian soldiers, about two years ago, occurring just miles from the attack, Fox News noted.
In addition to Niger and Mali, they include Chad, Mauritania and Burkina Faso.
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He said about 34 other persons were unaccounted for after the attack. France intervened in Mali in 2013 after extremists seized control of major towns in the north and implemented a harsh version of Islamic law.
Instead of hit-and-run raids by a small group of Kalashnikov-armed guerrillas, the jihadists are now carrying out operations that involve hundreds of fighters, armed with mortars and suicide vehicles.
Following Tuesday's attack, French President Emmanuel Macron and his Nigerien counterpart agreed to postpone a meeting of five presidents from the Sahel that had been scheduled for next week. But he added that a withdrawal of French troops from the region was not on the table.
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Malian government spokesman Yaya Sangare said on Wednesday that President Ibrahim Boubacar Keita would attend next Monday's meeting in southwestern France "under conditions" transmitted to France's envoy to the Sahel.