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.
The row highlighted sectarian divisions more than eight years after the 2003 U.S.-led invasion toppled the Sunni-led government of former dictator Saddam Hussein, who was hanged in 2006.
"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.
FIFA bans governments from meddling in national federations.
IFA had asked the world football body to be able to hold the new elections on June 16 but had so far received no reply. Unless FIFA confirms the election date, the vote cannot be held, the Iraqi federation official said.
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.
The country made an early exit from the 2010 World Cup qualifying competition, although they managed a 1-0 win over Australia along the way.
