The army killed "two terrorists following a clash with a dangerous" armed group in Jijel province, the ministry said in an initial statement, later revising the toll to three.
Algerian authorities use the term "terrorist" to describe armed Islamists who have been active in the country since the early 1990s.
The ministry said soldiers had seized weapons, ammunition and communications devices.
A day earlier, the defence ministry had announced the "surrender" of a heavily armed Islamist fighter it identified as Aissa Ben Khia, in Tin Zaouatine, in Algeria's far south.
A statement said the man, armed with a rocket launcher, three rockets, a machine gun and ammunition, had previously associated with "terrorist groups in 2018 near the border with Mali".
The army regularly announces the arrest or death of militants in different regions of the country.
In 2019, it said it had killed 15 armed Islamists and arrested 25 others, while another 44 had handed themselves in to authorities.
A civil war during the 1990s pitted Islamist militants against the Algerian government, leaving 200,000 people dead.
Despite a 2005 charter for peace and reconciliation designed to turn the page on the conflict, armed Islamist groups still remain active in some areas of the country, largely targeting security forces.
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