It was the second time parliament has delayed the presidential vote, which had first been due last week.
An AFP correspondent in the parliament said the required quorum was not reached on Sunday.
The vote was therefore delayed, according to the official INA press agency, which did not say whether a new date had been agreed.
The parliament's media office said the speaker will now meet the heads of party blocs to set a final date.
By convention, a Shiite Muslim holds the powerful post of prime minister, the parliament speaker is a Sunni and the largely ceremonial presidency goes to a Kurd.
The two main Kurdish parties have yet to settle on a presidential candidate, and the largest Shiite alliance -- despite backing Nouri al-Maliki for next premier -- faces US threats to end all support for Iraq if he takes up the post.
In Iraq, a country with chronically volatile politics driven by internal disputes and foreign pressure mostly from the United States and Iran, key decisions are often delayed beyond constitutional deadlines.
On Saturday, the Coordination Framework, an alliance of Shiite groups with varying degrees of links to Iran that has emerged as the main ruling coalition, said it "reiterates its support for its nominee", Maliki.
On Tuesday, US President Donald Trump declared Maliki a "very bad choice",and said that if Maliki was elected Washington "will no longer help Iraq".
Iraq's only two-term prime minister fell out with the United States during his premiership between 2006 and 2014 over growing ties with Iran.
Sources close to the Coordination Framework said that Shiite leaders are divided, with some wanting Maliki to stand aside, fearing US sanctions if he returns to office.
On the presidential front, Kurdish parties have yet to agree on a candidate, who must be endorsed by other blocs and win a two-thirds majority in parliament.
The presidency is usually held by the Patriotic Union of Kurdistan (PUK). This year, the rival Kurdistan Democratic Party (KDP) named its own candidate, Foreign Minister Fuad Hussein.
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