On Friday, Ibrahim al-Jafari leader of the Shia al-Dawa party met Ayat Allah Ali al-Sistani, who has been reported by Aljazeera to have given his blessing to the likely new prime minister.
After the meeting al-Jafari said: "There is an important issue we discussed: the participation of our brothers who could not take part in the election.
"The next government requires consultation and consensus."
Al-Jafari, who is the interim vice-president and leader of the Shia Dawa Party, and other politicians are jockeying for the top positions in the next government after last month's election, negotiations complicated by ethnic and sectarian issues in a country troubled by violence.
Leaders of Muslim Sunni Arabs who boycotted the election are not represented in the new government, after being Iraq's traditional leaders.
The election result has raised concerns disaffected Sunnis will join fighters waging a campaign of violence.
"There is an important issue we discussed: the participation of our brothers who could not take part in the election"
ButShia leaders have said Sunnis will play a role in Iraq's new political landscape despite their election turnout.
Whoever becomes prime minister is likely to make the country's security crisis the top priority.
Al-Jafari, a soft-spoken man who thinks dialogue can ease Iraq's problems, was nominated to be prime minister by the United Iraqi Alliance, which won the 30 January election.
The alliance will have a slim majority in the 275-seat National Assembly but must cut a deal to secure the two-thirds majority it needs to form a government.
A Kurdish coalition is in a strong bargaining position after coming second in the ballot and securing 75 seats.
The Kurds could give their backing to al-Jafari or the secular list led by Iyad Allawi, which clinched 40 seats after coming third and is determined to keep Allawi, a secular Shia, at the country's helm as prime minister.
No time limit
For his part, Kurdish leader Masud Barzani said on Friday that the Kurds had not decided whom to back.
Barzani(R) said Kurds would seek
key posts in the new government
There is no time limit for naming the top positions - a president and two vice-presidents, who must then decide on the prime minister.
Western diplomatic sources think it could take weeks to form a government.
Barzani, head of one of the two main parties in the Kurdish coalition, said the Kurds would seek key posts.
He was diplomatic but firm on the issue of Kirkuk, Iraq's most ethnically diverse and hotly contested city.
Kirkuk, 250km north of Baghdad, is near 6% of the world's known oil reserves and is split among Kurds, Arabs and Turkish-speaking Turkmen.
"In the future we want Kirkuk to be an example of ethnic, religious and national coexistence. But this is after Kirkuk's identity is fixed as (part of) Kurdistan," he said.