The cause of the crash was unclear, and an investigation has been opened, according to a Defence Ministry statement. The plane was carrying around 200 people.
Emergency services converged on the area near Boufarik after the crash, where smoke and flames could be seen rising from the wreckage.
The Defence Ministry did not provide a death toll but expressed condolences to the victims' families.
The secretary general of Algeria’s ruling FLN party, General Djamel, told private broadcaster Ennahar TV that the dead included 26 members of the Western Saharan Polisario independence movement.
The flight had just taken off from Boufarik, about 30 kilometres (20 miles) southwest of the capital Algiers, for a military base in Bechar in southwest Algeria, Achour said. It was scheduled to make a layover in Tindouf in southern Algeria, home to many refugees from the neighboring Western Sahara, a disputed territory annexed by Morocco.
The Soviet-designed Il-76 military transport plane crashed in an agricultural zone with no residents, Achour added.
Algeria has suffered a string of military and civilian aviation disasters.
Two military planes collided mid-flight in December 2012 during a training exercise in Tlemcen, in the far west of the country, killing the pilots of both planes.
In February 2014, 77 people died when a military plane carrying army personnel and family members crashed between Tamanrasset in southern Algeria and the eastern city of Constantine.
Only one person survived after the C-130 Hercules transport aircraft came down in the mountainous Oum El Bouaghi region.
The defence ministry blamed that crash on bad weather.
An Air Algerie passenger plane flying from Burkina Faso to Algiers crashed in northern Mali in July 2014, killing all 116 people on board including 54 French nationals.
In October the same year, a military plane crashed in the south of the country during a training exercise, killing the two men on board.
That came more than a decade after all but one of the 103 people on an Air Algerie Boeing 737-200 died in March 2003 when it crashed on takeoff in the country's south after an engine caught fire.