According to results obtained by Al Jazeera, al-Jaafari won 24 per cent of the vote, while al-Maliki got 10 per cent and Allawi secured nine per cent.
Jafaar al-Sadr, a cousin of the Shia leader who was on the ballot, secured 23 per cent of the 1.8 million ballots cast. Ahmad Chalabi, a member of the Iraqi National Alliance, got nine per cent.
Muqtada al-Sadr told Al Jazeera that he had turned down a recent offer by Daawa party that offered the release of his followers denaited by al-Maliki's government, in return for accepting an alliance with the state of Law coalition.
Al-Sadr sharply criticised al-Maliki and described his government as a failure.
"The new Iraqi government should be based on partnership, not on partisan, ethnic or sectarian bases," al-Sadr said in an interview with Al Jazeera.
Kingmaker
Though bereft of any legal authority, the two-day referendum was held after al-Sadr emerged as a kingmaker following Iraq's recently held national elections.
Zeina Khodr, Al Jazeera's correspondent in Baghdad, said: "They [Sadrists] have made the announcement, their choice is Ibrahim al-Jaafari...
"Sardist movement said they would abide by the choice of the people, which means more political uncertainty."
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The referendum results would contribute to more ambiguity to the Iraqi political scene which has been marred by the interpretation of the constitution regarding who should name the prime minister - the bloc which won more votes in the ballots or the one which govern the biggest number of seats in the parliament.
The results were a big disappointment for both Allawi and al-Maliki who wished to win the support of al-Sadr.
Final results in Iraq's March 7 elections gave the Allawi-led Iraqiya coalition just two seats more than State of Law bloc led by al-Maliki.
Shrewd move
The Sadrists won at least 39 seats in the 325-seat parliament making them the largest group within the Iraqi National Alliance (INA), a Shia coalition that placed third in the race.
Although the ballot was nominally open to all Iraqis, the vast majority of voters are likely to have been Sadrist backers.
The referendum was widely seen as a way for the Sadrist bloc, whose 30-something leader has been in Iran for about two years, to avoid giving its backing to al-Maliki.
"With this referendum, the Sadrists have made a shrewd move to put pressure on the other political parties," Hamid Fadhel, a Baghdad University political science professor, said.
"The negotiations with State of Law have stalled and the Sadrists want to push for someone other than Nouri al-Maliki [as premier], armed with popular support.
The Sadrists were key supporters when al-Maliki formed his government in 2006.
But two years later, he turned the security forces on the Mahdi Army, the movement's armed wing, jailing thousands of al-Sadr supporters in a campaign to destroy militias in the southern city of Basra and the Baghdad suburb of Sadr City.