Moqtada Sadr is emerging as a potential king-maker
The political grouping of the radical Iraqi Shia cleric, Moqtada Sadr, is holding its own referendum on who should be the country's prime minister.
The al-Sadr bloc is part of the Iraqi National Alliance, which came third in the parliamentary election on 7 March.
None of the four alliances that won the most seats can form a government on their own. Iyad Allawi's Iraqiya bloc came first with 91 out of 325 seats.
Since the vote, there has been little progress towards forming a government.
Representatives of Moqtada al-Sadr said the candidate who won a majority of votes in the referendum would get the backing of the 40 of his supporters who won seats in parliament.
The referendum, which has no legal authority, was open to all Iraqis, they added. Voting is scheduled to continue until Saturday.
"The political situation is complicated and [Moqtada Sadr] has always said that the best advisers are the Iraqi people," Hazem al-Araji, one of the movement's leaders, told the AFP news agency.
Correspondents say the two main contenders - Mr Allawi, a former prime minister, and the incumbent, Nouri Maliki, whose State of Law alliance won 89 seats - are highly unlikely to work together.
That leaves the the Shia-led Iraqi National Alliance (INA), which won 70 seats in total, as the king-makers, they add. The al-Sadr bloc won the majority of its seats.
The referendum offers a choice of five candidates, all of them Shias - Mr Maliki, Mr Allawi, former prime minister Ibrahim Jaafari, Vice-President Adel Abdel Mahdi, and Jaafar Mohammed Baqir Sadr, the cousin of Moqtada Sadr and son of the revered Grand Ayatollah Mohammad Sadiq Sadr, who was assassinated during the rule of Saddam Hussein.
The al-Sadr bloc is clearly against giving Mr Maliki a second term, and cynics have suggested the referendum is a way of formalising that position as the will of the people rather than the pursuit of a personal or political grudge, the BBC's Jim Muir reports from Baghdad.
Moqtada Sadr has not forgiven Mr Maliki for crushing his Mehdi Army militia in Basra and Baghdad two years ago, our correspondent says.
On Thursday, Ammar al-Hakim, the leader of the Supreme Iraqi Islamic Council - also part of the Iraqi National Alliance - said he would not join a governing coalition that did not include Mr Allawi.
Al-Iraqiyya (Iraqi National Movement): Nationalist bloc led by former PM Iyad Allawi, a secular Shia, includes Vice-President Tariq al-Hashemi, a Sunni Arab, and senior Sunni politician Saleh al-Mutlaq
State of Law: Led by Prime Minister Nouri Maliki and his Shia Islamist Daawa Party, the alliance purportedly cuts across religious and tribal lines, includes some Sunni tribal leaders, Shia Kurds, Christians and independents
Iraqi National Alliance: Shia-led bloc includes followers of the radical cleric, Moqtada Sadr, the Supreme Iraqi Islamic Council, and the Fadhilah Party, along with ex-PM Ibrahim Jaafari and Ahmad Chalabi
Kurdish alliance: Coalition dominated by the two parties administering Iraq's semi-autonomous Kurdish region - the Kurdistan Democratic Party and Patriotic Union of Kurdistan, led by President Jalal Talabani