After the fall of the Saddam regime, the army was officially disbanded, creating a large number of unemployed men.
The current appeal is part of a drive to build up a force to replace the current multinational troops, who are struggling with a bloody insurgency.
On Wednesday, at least 20 people died in a bombing in the town of Musayyib.
More than 45 people were also injured when a car exploded at sunset near a mosque, outdoor market and restaurant in the mainly Shia town, some 60km (40 miles) south of the capital Baghdad.
“The insurgents wanted to cause as many casualties as possible,” said Police Captain Muthana Khalid, who added that most of the victims appeared to be civilians.