The assailants opened fire on the men while they were working next to the main highway that runs through Kirkuk from Baghdad before fleeing, Jassim said.
A least 48 people were killed or found dead nationwide on Saturday, including a Sunni cleric who was shot near his home in Samarra, 95 km north of Baghdad.
George Bush, the US president, said he would send an additional 21,500 troops to help pacify the capital and other parts of the country in a plan for Iraq outlined on Wednesday.
Al-Maliki, however, continued to avoid naming al-Sadr's Mahdi Army as a target of the military operations.
"Our strategy that aims to control security is based on using force against any outlaws whatever their background or identity," al-Maliki said on state-run Iraqiya television.
Al-Maliki has repeatedly used that kind of formulaic language during his eight months in office, but has routinely blocked American forces from taking on his militia allies.
He told a small group of Iraqi reporters that "what we have seen in the American strategy is that it is identical to our strategy and our intentions".
A Kurdish army brigade in northern Iraq was undergoing intensive urban combat training as it readied for deployment in the latest Baghdad security operation and was expected to take on the capital's Mahdi Army Shia force, its commander said on Saturday.
Meanwhile, three Iraqi generals told The Associated Press that the Iraqi commander who will lead the overall Baghdad security mission was the government's second choice and only got the job after the US military objected to al-Maliki's first choice.
Nazir Assem Korran, commander of the 1st Infantry Brigade, 2nd Division of the Iraqi army, said: "We will head to Baghdad soon. We have 3,000 soldiers who are currently undergoing intensive training especially in urban combat and how the army should act inside a city."
Hillary Clinton, the US senator who opposes Bush's plans to send more US soldiers in to Iraq, met on Saturday with al-Maliki and the two top US commanders during her first visit in nearly a year.
The New York Democrat, who was expected to run for the party's presidential nomination, called the situation in Iraq "heartbreaking" and said she doubted the al-Maliki government would live up to promises it had made about cracking down on violence.
She said in an interview with ABC News in Baghdad: "I don't know that the American people or the Congress at this point believe this mission can work.
"And in the absence of a commitment that is backed up by actions from the Iraqi government, why should we believe it?"
"I'm sceptical that the Iraqi government will do what they have promised to do, and that, I think, is the concern of all of us who have heard this before," she said recalling at least three past security drives that have failed to calm the city.
The US military said on Sunday that five Iranians arrested by US forces in northern Iraq are connected to an Iranian Revolutionary Guard group that provides weapons to Iraqi militias.
The five were arrested on Thursday in a US raid on an Iranian government office in the Iraqi city of Arbil, the second such operation in a month.
The US military said in a statement: "Preliminary results revealed the five detainees are connected to the Iranian Revolutionary Guards - Qods Force (IRGC-QF), an organisation known for providing funds, weapons, improvised explosive device technology and training to extremist groups attempting to destabilise the government of Iraq and attack coalition forces.
"The Multi-National Force, in keeping with US policy, will continue to disrupt logistical support to extremists that originate from outside Iraq."