The army raided the old Hatin army base, now believed to be used by anti-US fighters, and found the corpses, said Captain Muhammad Abd al-Hussain al-Saidi.
The soldiers launched the operation after reports some Shia pilgrims on their way to the holy cities of Karbala and Najaf had disappeared near Latifiya, around 40km south of Baghdad, where fighters frequently launch attacks, al-Saidi said.
Corpses, the victims of attacks and banditry, turn up regularly across Iraq.
In December, 20 guardsmen were found lying dead in an area northwest of Mosul.
On 17 January, two Iraqi soldiers were discovered decapitated in Ramadi.
On 28 January this year, the bodies of four executed Iraqi soldiers were found dumped on a roadside in the city of Ramadi, west of Baghdad.
The decapitated bodies of three men, their heads strapped to their backs, were found dumped in nylon bags by a roadside north of Baghdad.