Iraq's Shia Prime Minister Ibrahim al-Jaafari said today that he was willing to withdraw his nomination for a second term if he was asked to step aside.
"If my people ask me to step aside I will do this," Mr Jaafari, who is under increasing pressure from Sunnis, Kurds and secular leaders to step aside, told a news conference after Iraq's first session was convened in Baghdad.
Mr al-Jaafari, who has been criticised for failing to curb violence, is also coming under mounting pressure from some of his partners in the ruling Shia Alliance, the largest block in parliament, which nominated him in an internal ballot.
In his comments, Jaafari did not specify who he was referring to when he said "my people." In previous public comments, Jaafari has said he had no plans at all to resign.
Wrangling over the premiership has delayed the formation of a government of national unity seen as the best chance to avoid a civil war as sectarian violence has escalated.
Earlier, Iraq's new parliament was sworn in with parties still deadlocked over the composition of the next government.
The long-awaited first session lasted just over 30 minutes and ended after failing to reach agreement on a permanent speaker for the legislature or on his deputies.
Members stood together and pledged to "preserve the independence and the sovereignty of Iraq and to take care of the interests of its people."
The opening of the first full-term parliament since the US-led invasion three years ago had been postponed due to disagreement over who should fill the senior positions.
Today's meeting should be the culmination of a political process that began with the overthrow of Saddam Hussein, but instead meets against a backdrop of continuing violence.
As a result, to satisfy a constitutional rule that the speaker be appointed at the first session, today's meeting did not formally adjourn, leaving the "first" sitting open for however long it takes to reach agreement.
Although the new constitution, ratified last year, sets a 30-day timetable for appointing a prime minister, there is a dispute over whether to apply it this first time around.
Today's session opened at 11 a.m. (8am Irish time) in the makeshift Convention Center premises of its predecessor in the fortified, so-called Green Zone in Baghdad.
With Washington anxious for a deal that it hopes can bring stability and let it bring its 133,000 troops home, US ambassador Zalmay Khalilzad has been shepherding party leaders into intensive talks this week on forming a government.