The C-130 Hercules aircraft, which came down in the Oum El Bouaghi region, was carrying 74 passengers -- soldiers and their families -- as well as four crew members, the ministry said.
The figure was far lower than the 103 people originally reported to be travelling on the C-130 Hercules transport aircraft by security sources and state media.
The ministry gave no immediate explanation for the discrepancy.
By early evening the emergency services had recovered 76 bodies from the crash site, including the remains of four women.
Also Read
President Abdelaziz Bouteflika announced three days of national mourning to begin tomorrow, praising the soldiers who perished in the crash as "martyrs."
The plane was flying from the desert garrison town of Tamanrasset in Algeria's deep south to Constantine, 320 kilometres east of Algiers, and lost contact with the control tower just as it was beginning its descent.
The aircraft slammed into Mount Fertas in the Oum El Bouaghi region at around midday (1100 GMT), state media quoted army spokesman Colonel Bouguern as saying.
Nearly 250 emergency personnel were deployed to the crash site despite the difficulties caused by the mountainous terrain and wintry conditions, the ministry added.
The recovery teams located one of the aircraft's two black box flight recorders, Algerian newspaper El Watan reported on its website.
Tamanrasset, where the flight had departed from, lies in the far south of Algeria, near the border with Mali, and is the main base for the country's southern military operations.