But lawmakers on Sunday, still facing the sticky questions of who gets what cabinet posts, did not name the nation's new president - likely Kurdish leader Jalal Talabani - and his two deputies.
They promised to tackle those issues on Wednesday.
Once named, the president and his deputies have two weeks to pick a prime minister, expected to be Shia politician Ibrahim al-Jafari.
While the candidates for president and prime minister were nailed down weeks ago, lawmakers had stalled over who would get key cabinet posts and how to reach out to Sunni Arabs, who largely boycotted the 30 January elections or stayed home because of fears of attacks.
Some criticised Sunday's choice of Industry Minister Hajim al-Hasani, one of only 17 Sunni Arabs in parliament, saying the new speaker did not represent the Sunni community.
Usama Abd al-Fatah, a 30-year-old architect, said al-Hasani's support last year of the US assault on the anti-US stronghold of Falluja showed he "does not have beliefs and will never do anything against his benefit".
The last parliament meeting on
29 March descended into chaos
Even though his Iraqi Islamic Party pulled out of the government over the issue, al-Hasani refused to leave his job.
"How could we just trust such a traitor?" Abd al-Fatah asked.
Former nuclear scientist Husain al-Shahristani, a Shia, and Kurdish official Arif Taifur were elected as al-Hasani's deputies.
The election on Sunday - carried out by secret ballot, with lawmakers allowed to choose up to three of five candidates - was a step towards rebuilding confidence in the nascent legislative body.
"It's time for the patient Iraqi people to be treated with the dignity that God has given them," al-Hasani said on Sunday, accepting his new post.
The results of the election were announced slowly, with each ballot read out loud and every vote tallied, one by one, with a black marker on a white board.
Officials said 28 of parliament's 275 members never showed up for Sunday's session, including outgoing interim Prime Minister Iyad Allawi, who was not in Baghdad. Others came after the session started, including five legislators who arrived too late to vote.
Baghdad has recently witnessed
an increase in security measures
Many said blocked streets and increased security measures kept them from arriving on time.
Shortly after the votes were tallied, an apparent mortar round fell near where the lawmakers were meeting. No casualties were reported.
Some lawmakers in the assembly meeting called for the release of detainees in US military prisons, one day after dozens of fighters attacked the Abu Ghraib prison in western Baghdad with car bombs, gunfire, and rocket propelled grenades.
The 40-minute clash killed one fighter and wounded 44 US forces and 13 prisoners, US military officials said.
An internet statement purportedly made by al-Qaida's wing in Iraq admitted responsibility on Sunday. It could not be independently verified.
Some soldiers were evacuated with serious injuries, officials said.
The US military is holding about 10,500 prisoners in Iraq, with 3446 at Abu Ghraib.
Pentagon says 1537 US soldiers
have been killed in Iraq so far
In other developments, the US military said on Monday a US soldier had been killed by a roadside bomb in central Iraq.
The explosion occurred near Baiji, an oil-refining town about 200km north of Baghdad, on Saturday. No other details were provided.
Earlier, the US military announced the deaths of two service members: a marine killed by an explosion in combat operations a day earlier in the central city of Haditha, and a soldier killed on Sunday by a homemade bomb.
In the northern city of Mosul, two car bombings left at least one Iraqi civilian dead and several others injured, while Khalid Jirrawi - the spokesman for the Patriotic Union of Kurdistan, one of the two main Kurdish parties in Iraq - said a Kurdish soldier was killed when armed men opened fire on his car.
The US military also released details of an investigation that confirmed a Bulgarian soldier was killed last month by friendly fire during a clash with US soldiers.
The investigation found that Bulgarian soldier Gurdi Gurdev was fatally wounded on 4 March in southern Iraq, when US and Bulgarian forces "fired on each other in response to what each believed to be a hostile act from a legitimate military target", according to a statement released by the US military.
"It's time for the patient Iraqi people to be treated with the dignity that God has given them"
Iraqi Parliament Speaker
Also on Sunday, representatives of Arab and Islamic communities in Bucharest, Romania, appealed to the abductors of three Romanian journalists to release them.
In a statement that was sent to Aljazeera, the representatives described the journalists as messengers of truth, and urged that they be freed to return home safely.