Political bickering has paralysed the federation, split by sectarian divisions seven years after the U.S-led invasion and three years after a multi-ethnic Iraqi squad won the Asia Cup.
FIFA requires governments to refrain from meddling in national football federations and has suspended Iraq twice, lifting the latest ban in March on condition the federation agreed on a road map for new elections.
The government of Shi'ite Prime Minister Nuri al-Maliki has been trying to remove top officials from sport bodies suspected of ties to the Sunni-led former government of Saddam Hussein.
Hussain Saeed, president of the Iraqi Football Association who once was a senior official on the Olympic Committee controlled by Saddam's son Uday, is facing a challenge from Falah Hassan, backed by the Shi'ite-led government. Both are former players in the Iraqi national team.
"We failed to conduct the vote due to a lack of quorum and ask FIFA to grant a postponement until conditions improve," Saeed told reporters.
The bickering has affected Iraq's performance after hiring a succession of coaches and failing to qualify for the World Cup in South Africa this year. Last year, FIFA allowed Iraq to host its first friendlies since 2003. Iraq defeated Palestine in two matches played in Arbil and Baghdad.
