The violence erupted when armed men stormed a local office of the agriculture ministry in the city's south, the interior ministry said.
Police forces responding to the scene "came under fire", resulting in several injuries among security personnel, the ministry added.
Iraq's Joint Operations Command, which coordinates between security forces and the military, said 14 suspects were detained who belonged to the Hashed al-Shaabi, a network of former paramilitary units that have been integrated into the regular security forces.
Several other security sources, however, told AFP that the armed men were affiliated with the powerful pro-Iran group Kataeb Hezbollah, a faction within the Hashed al-Shaabi that sometimes acts on its own.
Kataeb Hezbollah had opposed a recent appointment at the agriculture office, which is located in an area where the group holds influence, the sources said on condition of anonymity as they were not allowed to speak to the media.
"One policeman was killed" and others were wounded, said one official.
Another security source said one policeman and one civilian were killed.
A member of Kataeb Hezbollah said that a fighter from the group was also killed and six others wounded.
He added that the group "does not want to escalate", and would allow the judiciary to take its course.
After decades of war and turmoil, gun battles -- sometimes sparked by minor feuds -- are not uncommon in Iraq, where many armed groups operate.
Iraq is led by an Iran-aligned coalition called the Coordination Framework, which brings together Shiite Islamist parties and factions of the Hashed al-Shaabi.
Prime Minister Mohammed Shia al-Sudani has ordered a probe into the incident at the agriculture office.
The interior ministry said "it would not tolerate any party attempting to impose its will by force and threaten state institutions".
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