Iraq's Prime Minister Ibrahim Jaafari says he is willing to withdraw his nomination to lead the new government if the Iraqi people want him to do so.
Most parties do not want Jaafari continuing as prime minister
"If my people ask me to step aside I will do this," Mr Jaafari said, shortly after attending the much-delayed inaugural session of Iraq's parliament.
The Shias' nomination of Mr Jaafari has been a major sticking point in forming a government as he lacks wider support.
He has been criticised for not doing more to curb Iraq's violence.
Growing sectarian violence in the country has prompted predictions that Iraq is on the brink of civil war.
Despite the first session of parliament being brought forward by three days from its postponed date, the BBC's Jim Muir in Iraq says this is not a sign of accord.
It is three months since the election, and unresolved differences between the parties are likely to delay the formation of a new government for several more weeks at least, our correspondent says.
The inaugural session lasted just 30 minutes as wrangling over power meant members were not even able to elect a speaker. The job is part of a wider power-sharing package.
Political sources say one idea that has been agreed in principle, partly because of heavy pressure from the US ambassador, is the formation of a new leadership council.
This would be made up of the president, the prime minister, the speaker of parliament, the head of the judiciary and political chiefs.
Its exact function - and even its title - have not been agreed, but if it does see the light of day, it might help take some of the heat out of the debate over who should be the next prime minister, our correspondent says.
The 275 members were sworn in during the session
Iraqi and international observers believe a national unity government is the only hope of saving the country from worsening civil strife and will help lessen insurgent attacks.
The streets of the capital were quiet as the parliament held its first session thanks to a vehicle ban introduced in an effort to curb car bombings.
Appeal for calm
The meeting was held inside a convention centre behind the concrete blast walls of Baghdad's heavily fortified Green Zone.
The ceremonial session, in which the 275-members of parliament were sworn in, was broadcast live on Iraqi television.
It began with a recitation of the Koran, followed by a minute of silence in memory of Iraqis who gave their lives in the struggle against the Baathist regime of former President Saddam Hussein.
Adnan Pachachi, the oldest member, addressed those gathered, urging Iraqis to avoid a civil war.
"The country is going through very difficult times and it faces a big dilemma after the Samarra bombing and the attacks that followed. Sectarian tension has increased and it threatens national disaster," Mr Pachachi said.