"Today at 1050 (0950 GMT) in the border area of Timiaouine, a detachment of the ANP (army) was the target... of a suicide attacker in an all-terrain vehicle," the statement said.
"The soldier in charge of access managed to stop the suspect vehicle from entering, however the suicide attacker blew up the vehicle, causing the death of the solider on guard," it added.
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No information was given about the identity of the attacker.
Acting Deputy Chief of Staff Said Chanegriha offered condolences to the family of the "martyred" soldier, and praised "the great vigilance shown by the unit which was able to foil this desperate attempt for media attention."
Chanegriha stressed "the determination of ANP forces to eradicate the scourge of terrorism and to track down criminals across the country, to preserve the security and stability of the state."
The attack -- which was not immediately claimed -- is the first of its kind in southern Algeria in years.
In January 2013, members of al-Qaeda attacked a gas plant near In Amenas near the Libyan border. Forty hostages died along with 29 militants.
Sunday's attack comes as Algeria is seeking involvement in attempts to resolve regional crises in Libya and the Sahel.
Worried by the risk of instability in southern Algeria, Algiers served in 2014 and 2015 as mediator between the Malian government and armed rebels.
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The last suicide attack against Algerian forces was in August 2019.
Two Algerian police were killed when a suicide bomber detonated his vest while trying to enter a police station in Tiaret, 250 kilometres (155 miles) southwest of Algiers.
The militant Islamic State group claimed that attack.
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