Moves to form a new government are under way in Iraq after the announcement of full election results.
The winning Alliance is dominated by Grand Ayatollah Ali Sistani
The Shia United Iraqi Alliance (UIA) says it wants to name a new prime minister after it was confirmed as winning nearly half the vote.
However, the bloc will not have a parliamentary majority on its own. Kurdish groups, which came second, are seen as potential partners.
The process of forming a coalition is likely to take several weeks.
The finance minister in the interim government, Adel Abdel Mahdi, is widely tipped as the UIA's candidate for prime minister.
One of the new parliament's main jobs will be to write a constitution, but the representation of the Shia bloc falls far short of the two-thirds majority needed for that.
The BBC's Jon Leyne in Baghdad says there are many deals to be done in the coming weeks.
"Iraq is bleeding and we need everybody at this juncture to work for solidarity and unity," Mr Abdel Mahdi told Arabic TV channel al-Arabiya.
He added that his alliance - which is backed by Iraq's most senior Shia Muslim cleric Grand Ayatollah Ali Sistani - was "seeking to realise a wide national harmony" in choosing key positions.
The Kurds have meanwhile called for one of their leaders - Jalal Talabani - to become president.
Mr Talabani on Monday urged the inclusion of Sunni Arabs in any debate about the future constitution.
"The permanent constitution must be formulated on the basis on a consensus among the Sunni Arabs, the Shia Arabs and the people of Iraqi Kurdistan," he told Lebanese television.
"It is impossible to marginalise or ignore the Sunni Arabs in Iraq."
According to results released by Iraq's election commission on Sunday, 58% of registered Iraqis turned out to vote in the 30 January poll and the Shia alliance took 48% of ballots cast.
A secular list led by Prime Minister Iyad Allawi got 14%, while ethnic Kurdish parties won 26%.
The results were described as provisional, since parties were given three days to lodge any appeals.
Our correspondent says the new leaders must also decide how much real power to share with Sunni Muslims, who dominated Iraq before the US-led war that ousted Saddam Hussein.
Sunni candidates won only a handful of seats in the new parliament, because of an election boycott and intimidation.
The violence continued after the poll. On Sunday at least nine people died in attacks across Iraq.
TIMETABLE FOR GOVERNMENT
14-16 February: Complaints dealt with
Early March: PM appointed
Late March: Government formed
15 August: Draft constitution (six-month extension possible)
15 October: Possible referendum on constitution
By 15 December: Elections for government
US President George W Bush on Sunday congratulated Iraqi voters "for defying terrorist threats and setting their country on the path of democracy and freedom".
The US and its coalition partners could "all take pride in... making that great day possible", he added.
UK Foreign Secretary Jack Straw said Iraq had taken another important step towards a democratic future.
The European Union congratulated the winners and urged them to ensure they governed in the name all Iraqis.
"I trust they will ensure full representation of Iraq's diverse society in the political process, and in particular in the drafting of the constitution," said EU external relations commissioner Benita Ferrero-Waldner.
Among Iraq's neighbours, Jordan said the next step must be to consider all parties and their representation.