The main Shia alliance in Iraq has postponed a meeting to decide whether to replace Ibrahim Jaafari as its candidate for prime minister.
Talks are deadlocked over Mr Jaafari's nomination
The United Iraqi Alliance said the meeting would take place on Tuesday.
Earlier, Sunni Arab and Kurdish groups re-affirmed their opposition to Mr Jaafari remaining in his post.
They have argued that Mr Jaafari is not a sufficiently neutral or non-sectarian figure to lead what is expected to be a government of national unity.
A United Iraqi Alliance official told the BBC the alliance was due to receive a report from the three-member committee that has been sounding out the strength of opposition among other parties to Mr Jaafari.
The issue is impeding the creation of a government, three months after polls.
BBC Baghdad correspondent Mike Wooldridge says the Shia parties have also come under growing pressure from the United States to drop their support for Mr Jaafari.
Even some top Shia clerics are pushing for a swift solution amid warnings Iraq is approaching civil war.
Determined to stay
Many hope a government that unites the majority Shia bloc and the smaller Sunni and Kurdish groups will be best placed to tackle a recent rise in sectarian violence.
The Iraqi Shias' spiritual figurehead, Ayatollah Ali al-Sistani, has joined other Shia figures in pushing for the speedy formation of such a government.
But Mr Jaafari, who is the interim prime minister and commands considerable support among some Shia factions, has said he is determined to remain in office.
Correspondents say the Shia alliance will have to decide if it will stick with Mr Jaafari - thereby most probably prolonging the current deadlock - or whether it will nominate someone else from its ranks.
'More names needed'
The Kurdish leader and Iraqi president, Jalal Talabani, said on Sunday that opposition to Mr Jaafari was unlikely to soften.
Many hope a political deal will help to end the violence
"I think the majority of other groups, or all the other groups, are rejecting Dr Jaafari as prime minister," he told the BBC.
Iraq's main bloc of Sunni parties affirmed on Monday that it too rejects Mr Jaafari.
A spokesman for the group said it will ask the Shia alliance "to present names for other candidates".
Kurdish and Sunni politicians have accused Mr Jaafari of monopolising power and exploiting sectarian tensions.
Under Iraq's constitution, the prime minister has to be drawn from the ranks of the group that won the most seats in elections.
Though they are the largest group, the Shia alliance still needs the support of other parties to govern.
Dispute over 'civil war'
Mr Jaafari appeared before reporters on Sunday to dismiss suggestions made by Egypt's Hosni Mubarak to al-Arabiya TV that a civil war "was on the doorstep".
However, Iraq's leaders themselves appear to be divided on the issue.
Speaking a day after suicide bombings in a Baghdad mosque left 90 dead, the deputy interior minister told the BBC on Saturday the country had been in a state of undeclared civil conflict for a year or more.
Sectarian tensions have been high since the bombing of a Shia shrine in Samarra in February.
The US military has said 1,313 Iraqi civilians were victims of sectarian violence in March. Some analysts believe the real figure is much higher, as many bodies are never found.