Saeed, who has been living outside the war-battered country, wrote a letter submitting his resignation which which must be formally accepted by the IFA executive, a federation official said on Tuesday.
Saeed still remained on the candidate list for the post, he added.
In August last year, football's world governing body FIFA gave the Iraqi federation a year to settle a bitter political row which had blocked the leadership elections and put Iraq at risk of being suspended from international competition.
"To open the way for Iraq's football to march ahead away from political and sectarian interference, the ghost of which I see starting to penetrate our family... I have decided to resign from the presidency," Saeed said in his letter.
Once one of Iraq's best-known football players who had also served as national coach, Saeed had been a member of the Olympic Committee controlled by Saddam's son Uday.
The Iraqi government of Shi'ite Prime Minister Nuri al-Maliki has been trying to remove top officials from sport bodies suspected of having ties to the Saddam regime and its once ruling Baath party.
Saeed had accused Maliki's government, which backs a rival candidate, of interfering with the federation elections and last year requested FIFA to allow IFA to postpone them.
Iraq captured the world's imagination by winning the Asian Cup in 2007 but have struggled since then and have employed a succession of coaches.
