The continued failure by parliament to select a president after last year's elections reflects a deep schism between Shiite political groupings, with one bloc boycotting proceedings.
"The assembly adjourned its session until further notice," the parliament's press service said without giving a new date.
Iraq's federal court has given lawmakers until April 6 to choose a new president.
If that deadline is missed, said political scientist Hamza Haddad, "we could reach a point where new elections are decided to break the deadlock".
The judiciary can only determine "a violation of the constitution" and cannot take any initiative to break the political deadlock, according to legal expert Ahmed al-Soufi.
A parliamentary source told AFP that only 178 out of 329 lawmakers were present in parliament Wednesday, far short of the two-thirds quorum required for the vote.
As in the previous two aborted votes, last Saturday and February 7, Wednesday's session was boycotted by a major Shiite coalition bloc in parliament.
Half a year after October 2021 legislative elections, Iraq still does not have a new president or prime minister, keeping the country in a state of political paralysis.
Parliamentarians must first elect the head of state, by convention a member of the Kurdish minority, with a two-thirds majority. The president then appoints the head of government, a post still held by Mustafa al-Kadhemi, who headed the previous government.
'LITTLE APPETITE'
Among the 40 candidates for the presidency, two are considered the frontrunners: incumbent Barham Saleh, of the Patriotic Union of Kurdistan (PUK), and Rebar Ahmed of the rival Kurdistan Democratic Party (KDP).
On February 13, Iraq's supreme court ruled out a presidential bid by KDP-backed veteran politician Hoshyar Zebari, after a complaint filed against him over years-old, untried corruption charges.
Iraqi politics were thrown into turmoil following October's election, which was marred by record low turnout, post-vote threats and violence, and a months-long delay before the final results were confirmed.
The largest political bloc, led by firebrand Shiite cleric Moqtada Sadr, had backed Zebari for the presidency before moving its support to Ahmed.
The failed votes in parliament have underscored the gulf in Iraqi politics between Sadr, the general election's big winner, and the powerful Coordination Framework, which called the boycotts.
The Coordination Framework includes former premier Nuri al-Maliki's party and the pro-Iran Fatah Alliance -- the political arm of the Shiite-led former paramilitary group Hashed al-Shaabi.
Alongside backing Ahmed for the presidency, Sadr intends to entrust the post of prime minister to his cousin and brother-in-law Jaafar Sadr, Iraq's ambassador to Britain.
That prospect is unpalatable for the Coordination Framework.
Sadr on Wednesday ruled out any compromise, warning that a consensus government would spell the "death" of Iraq.
