BAGHDAD — Iraq’s political disarray deepened Wednesday when a potential kingmaker withheld his support from both big election winners and said he would ask his supporters to make the choice in a referendum.

Compounding the confusion, the incumbent prime minister refused to abandon his claim of fraud and his demand for a recount.

A coalition led by secular challenger Ayad Allawi, a Shiite who drew on deep Sunni support, eked out a two-seat lead over a mainly Shiite bloc led by Prime Minister Nouri al-Maliki in results released last Friday.

That gave a pivotal role to Muqtada al-Sadr, a Shiite and powerful anti-American cleric, without whose support neither Allawi nor al-Maliki would have difficulty forming a coalition.

Al-Sadr’s hardline, religious Shiite party, which won 39 of the 325 parliamentary seats in the March 7 election, has emerged as a key powerbroker whose support will prove crucial in determining which of the two leading blocs will form the next government.

While the Sadrists ostensibly belong to a Shiite religious bloc which has supported al-Maliki in the past, they have a deep-rooted animosity for him after he jailed thousands of their supporters and routed their militias in Basra and eastern Baghdad.

So far they have opposed joining any coalition in which al-Maliki would be the prime minister.

The referendum would give the Sadrist leadership an excuse not to support al-Maliki and openly back another candidate under the guise of following what the people want.

“It’s more sort of symbolic and populist and trying to display a measure of strength, and also to say that our position is a reflection of the will of the people,” said Michael Hanna, an Iraq analyst with the New York-based Century Foundation.

The poll is also another sign of the young cleric’s growing political clout within this Shiite-dominated country, and adds to the Sadrists’ appeal among many Iraqis frustrated with a political system in which much of the negotiations and decision-making happens behind closed doors.

A spokesman for al-Sadr, Salah al-Obeidi, said Wednesday that the referendum results would be binding on the party.

The voting would be Friday and Saturday at al-Sadr offices, mosques and other sites across the country. Al-Sadr first called for the referendum Tuesday on his Web site.

People taking part in the poll would be allowed to choose from five candidates, including al-Maliki and Allawi and be allowed to write in someone of their choosing.

Al-Obeidi said all Iraqis would be allowed to take part in the poll.