Under an informal system that took root after the 2003 U.S.-led invasion that ousted Saddam Hussein, the prime minister's job goes to a Shiite, the president's post to a Kurd and the speaker of parliament's chair to a Sunni.
The main point of contention right now is the post of prime minister, which holds most of the power in Iraq.
Incumbent Nouri al-Maliki, whose State of Law bloc won the largest share of seat in April's election, has vowed he will not abandon his bid for a third consecutive term. But he didn't win a majority in parliament and so needs allies to form a government, setting the stage for what now appear to be protracted political negotiations.
Al-Maliki is facing pressure to step aside, in part because many in the country accuse him of monopolizing power and contributing to the current crisis by failing to promote reconciliation with the country's Sunni minority.
The militant offensive spearheaded by the Islamic State extremist group has tapped into the Sunni community's grievances with al-Maliki's Shiite-led government. Sunnis complain of being marginalized and unfairly targeted by the security forces.
After its initial blitz, the insurgent onslaught has eased since overrunning most of Iraq's Sunni-dominated areas. But fighting rages daily on several fronts across the country.
One of the most active zones is the Sunni-dominated region west of Baghdad, where on Monday a mortar shell landed near Iraqi troops during a raid on the village of Karma, killing Iraqi army 6th Division commander Maj. Gen. Najim Abdullah Ali.
Ali was overseeing the raid when the round exploded nearby, army spokesman Brig. Gen. Saad Maan Ibrahim said.
Al-Maliki lamented Ali's death, calling him a "holy warrior" who was "martyred in the battlefield as he was fighting the terrorists."
Sunni militants seized control of the city of Fallujah, near Karma, and parts of the provincial capital of Ramadi in January. The government has since reasserted its control of Ramadi, but Fallujah remains in insurgent hands.
In Baghdad, a suicide bomber rammed a vehicle packed with explosives into a checkpoint in the Shiite neighborhood of Kazimiyah, killing five policemen and three civilians, a police official said. He said 16 people were wounded.
A medical official confirmed the casualty figures.
Both officials spoke on condition of anonymity as they were not authorized to release information.