Iraqi officers who served under the regime of Saddam Hussein are being invited to rejoin the army.
The army was dissolved after the regime fell
The force was disbanded after the US-led invasion in 2003 - a move seen by many as an error as it created large numbers of unemployed, disaffected men.
The appeal is part of a drive to build up a military to replace the current multinational troops, who are struggling with a Sunni-led insurgency.
On Wednesday, at least 20 people died in a bombing in the town of Musayyib.
Soldiers who served under the former regime have been gradually rejoining since 2004, but the army still has a shortage of qualified, experienced officers.
Under the new drive, officers up to the rank of major are being asked to apply.
Each rank will have a five-day period over the next month to sign up at recruitment centres across in the country. They will undergo medical tests and interviews.
Laith Kubba, the Iraqi government spokesman, said the step was "a bold move to turn the page" as the country moves ahead having approved the new constitution last month.
He told the BBC there had been an "illusion" after the fall of Saddam Hussein that a new Iraqi army could be built in a short period of time.
"This has not happened," he said, adding that there were "many indications" that the sacked officers of Saddam Hussein's regime had become part of the insurgency problem.
The BBC's Defence Correspondent Rob Watson says this is a very significant move for Iraq's defence ministry.
He says it represents a major effort to reach out to Sunnis in an attempt to build a national, more-inclusive army.
Such a force would also make it easier to patrol areas where the insurgency is strongest, such as the Sunni-dominated west of the country, if the forces deployed included Sunni soldiers.
The former Iraqi army was disbanded in 2003 by the then US administrator in Iraq, Paul Bremer, a move seen by many observers as simply playing into the hands of insurgents.
The police and armed forces now number about 200,000 - two-thirds of the total number sought, Iraqi officials say.
But even if the recruitment campaign is successful, it is unlikely to solve all the problems facing the current army, which is also plagued by infiltrators and poor equipment, our correspondent adds.
The attack in the mainly Shia town of Musayyib, some 60km (40 miles) south of the capital Baghdad, came just before sunset. At least 45 people were injured.
A minibus exploded near a mosque and market as people attended prayers to mark the end of the daily fast on one of the last days of the month-long Muslim festival of Ramadan.
The market would also have been particularly busy as Iraqis prepare for the three-day Eid al-Fitr holiday later in the week.
Elsewhere on Wednesday, two US servicemen died near the western city of Ramadi after their helicopter crashed. The cause of the crash is being investigated, says the US military.