Iraqi Prime Minister Ibrahim Jaafari has asked the main Shia coalition to confirm his candidacy in a bid to break the deadlock over a new government.
Mr Jaafari insists his nomination is Iraq's democratic choice
Mr Jaafari's candidacy is rejected by Sunni Arabs, Kurds and others and some members of his own coalition.
Until now he has refused repeated demands to stand down.
Parliament was due to meet for its second session on Thursday, but it was postponed to allow the United Iraqi Alliance to consider Mr Jaafari's fate.
BBC correspondent Jim Muir says the hope is that the UIA will pick a new nominee acceptable to all parties, so that the government formation can go ahead swiftly - or it could renominate Mr Jaafari.
The political conflict has defied efforts by the US and UK to put pressure on the factions to set up a unity government - something all sides agree is necessary to end the instability and violence that has beset Iraq since the US-led invasion in 2003.
Parliament was due to convene 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 was threatening to boycott the session unless its candidate for prime minister is accepted.
A spokesman for Mr Jaafari's Dawa party said the alliance would meet on Thursday or Friday to decide the renomination request.
Mr Jaafari won an internal coalition election by the slimmest of margins in February.
Since then, he has insisted his nomination was the democratic choice of the Iraqi people, and has refused to step down.