Iraq's largest parliamentary bloc will hold a fresh internal vote to nominate a candidate for PM, hoping to break months of damaging political deadlock.
Iraq's politicians have been under pressure to put aside differences
It follows Ibrahim Jaafari's offer to resubmit his candidacy to the United Iraq Alliance - a coalition led by religious Shia Muslim parties.
Mr Jaafari narrowly won the nomination in February but faced strong opposition for his alleged sectarian attitude.
Parliament has again delayed meeting while the UIA considers its leader.
It is the second time in a week that a planned session has been postponed. The body will now meet on Saturday.
"I believe if we give ourselves this time, we will be able to succeed in forming a national unity government which people have been waiting for," acting speaker Adnan Pachachi told reporters.
Sunni, Shia and Kurdish parties have been caught in a deadlock for months over Mr Jaafari's nomination, preventing the creation of a government at a time of increasing sectarian violence.
A national unity government is seen as the only way to stop violence
But the BBC's Jim Muir in Baghdad says hopes are rising for an end to the impasse.
The US and UK have been putting pressure on Iraq's political factions to set up a unity administration - something all sides agree is needed to end the instability and unrest gripping Iraq since the US-led invasion in 2003.
In the latest violence:
- Two policemen are killed in a roadside bombing against a passing patrol in Khalis, north-east of Baghdad
- Another policeman is killed in a similar attack in Baquba, in the same area
- Four civilians are killed by gunmen in and around Baquba
- Two civilians are killed in a car bomb attack near a British army patrol in southern Iraq
- An interior ministry general escapes injury when a roadside bomb hits his convoy in Baghdad, killing one civilian
- There are unconfirmed reports of at least 12 other killings in various parts of Iraq.
Parliament had been due to convene on Thursday for only the second time since it was elected in December, to chose a speaker, who is likely to be drawn from the Sunni Arab parliamentary contingent.
But the UIA threatened to boycott the session unless its candidate for prime minister was also accepted.
A spokesman for Mr Jaafari's Dawa party said the alliance would meet on Thursday or Friday to decide the re-nomination request.
As recently as Wednesday, Mr Jaafari was refusing to step aside, insisting his nomination was the democratic choice of the Iraqi people.
Correspondents quote MPs saying that a meeting with United Nations envoy Ashraf Qazi and Shia Muslim religious leaders were key factors in Mr Jaafari's change of heart.