The session opened with a prayer and an orchestral performance of the national anthem, as lawmakers convened for the first time since national elections were held in May.
The new parliament faces the twin tasks of rebuilding the north of the country following the war against the Islamic State group and rehabilitating services in the south, where severe water and electricity shortages have fueled protests.
"We must focus in the next stage on reconstruction, services, and providing jobs. It is the time for economic reforms and expanding our security achievements," said caretaker Prime Minister Haider al-Abadi in an address to parliament.
Al-Abadi, who came to power in 2014, oversaw the war on IS after the extremists seized Mosul, Iraq's second largest city, and close to one-third of Iraqi territory.
Al-Abadi declared victory last year, but the militants continue to raid, kidnap, and murder Iraqis in lawless and underserved regions in the west and center of the country.
Lawmakers must now select a parliament speaker before electing a president, a largely ceremonial post. The president then appoints a prime minister, nominated by the largest bloc in parliament, to form a government.
Two blocs are claiming the right to name the prime minister.
A coalition led by al-Abadi and populist cleric Moqtada al-Sadr has the support of the U.S. and Saudi Arabia, while an alliance between former Prime Minister Nouri al-Maliki and militia leader Hadi al-Amiri has the backing of Iran.
Both alliances are dominated by Shiites, who have held the preponderance of power in Iraq since Saddam Hussein's ouster in 2003. But the largest Sunni blocs are aligned with al-Abadi and al-Sadr. Iraq's two main Kurdish parties have not taken a side.
By custom, the prime minister's post is reserved for Shiites, the speaker's post for Sunnis, and the presidency for Kurds.
On Monday, the al-Maliki bloc presented a statement with 150 signatories from the 329-member Parliament saying they had formed the largest grouping in the legislative body.
The al-Abadi bloc attested in a document to the legislative body that it had more than 160 members in its caucus, though their statement contained only a handful of signatories.
Lawmaker Qateh al-Rukabi said the matter would likely be taken to Iraq's highest court for a ruling.
Al-Maliki is said to be trying to woo lawmakers from al-Abadi's bloc. Al-Maliki and al-Abadi are both leading members of the Islamic Dawa party, which remains divided over the longstanding rivalry between the two men.
Mohamad Ali Zeini, parliament's oldest lawmaker and its caretaker speaker, adjourned the session until Tuesday to allow members time to choose a speaker.
He told The Associated Press he was doubtful a quorum would be achieved Tuesday as Sunni lawmakers were divided between 6 nominees.