Critics of the Maliki government say that its relentlessly sectarian policies alienated Sunnis, helping to ease the way for the Islamic State in Iraq and Syria to oust the Iraqi Army and move into Sunni areas in Iraq’s north and west. In the melee, the Kurds seized other disputed areas in the north with the result that the country’s borders are being redrawn on the ground, something that many Iraqi lawmakers seem not to have fully faced.

Instead, much of the public discussion has been about assigning blame for not forming the government, while there is almost certainly considerable bargaining going on behind closed doors about what each bloc needs to sign on to the leadership slate.

“The session was postponed until Aug. 12 because of the disagreement and the conflict between the blocs,” said Aboud al-Essawi, a member of Mr. Maliki’s predominantly Shiite State of Law party, referring to other political parties.

The Sunnis said they were ready to proceed, but wanted the Shiites to make the first move. “We are still saying that we are ready to present our candidate for speaker whenever the National Alliance presents its candidate for prime minister, and it can be anyone else but not Maliki,” said Dafar al-Ani, a spokesman for the main Sunni bloc, referring to a coalition of Shiite parties.

“The National Alliance asked for more time to make their final decision,” he added.

Beneath the blame game are real differences in what is acceptable to different groups. For instance, a large number of Shiites now want to remove Mr. Maliki, but his party won the most parliamentary seats, so he cannot be summarily kicked aside. And there are differences of opinion about who might be an acceptable successor, first to all the Shiite blocs, but then also to the Sunnis and the Kurds.

Image Brig. Gen. Najim Abdullah Ali al-Sudani. Credit... Ahmed Saad/Reuters

Mr. Maliki says that removing him just as Iraq is trying to reconstitute its demoralized army would undermine those in the fight. While that might seem a convenient argument to prolong his time in power, at least some lawmakers appear to agree.