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Federation President Sahilu Gebremariam said the entire leadership, including himself, would not seek re-election in September.
"(We) don't wish to continue," Sahilu said.
Although the committee members did not all separately say they would be stepping down, first Vice President Teka Asfaw said he also would stand down.
FIFA is investigating Ethiopia for fielding an ineligible player in the World Cup qualifier in Botswana on June 8, which the Ethiopians won 2-1.
Although FIFA didn't name the player under suspicion, the federation has admitted that Minyahile Beyene should not have played because he was suspended for receiving two yellow cards in previous games, but officials "forgot" about the suspension.
Following an emergency meeting on Monday, Sahilu also said that the federation's secretary general had been fired and a vice president in charge of the national team had offered his resignation.
Ethiopia could forfeit the three points it collected for beating Botswana if FIFA finds it guilty of fielding an ineligible player, meaning it would not yet be guaranteed a place in the final 10-team playoffs in Africa's qualifying competition.
Ethiopia, which has never been to the World Cup, beat South Africa 2-1 in its most recent qualifier and believed it had qualified for the playoffs with that victory.
However, if FIFA deducts three points, Ethiopia would only be two points ahead of South Africa in Group A ahead of one more round of group games.
South Africa also reportedly asked FIFA to dock Ethiopia a further three points because Minyahile played again in their qualifier on June 16.
The City Press newspaper in South Africa said Sunday that the South African Football Association had sent two letters to the world body, asking it to investigate Minyahile's participation in that game and an unconnected alleged spitting incident involving South Africa midfielder Dean Furman.
Furman claimed on Twitter that an Ethiopian player had spat in his face.
"I've seen some things in the game but to be spat in the face by another player is the lowest of the low," Furman wrote.
FIFA is investigating Togo and Equatorial Guinea for also allegedly fielding ineligible players in World Cup qualifying, meaning another two World Cup qualifying groups in Africa could be thrown into chaos if the teams are stripped of their victories and the points awarded to their opposition.
FIFA typically awards the opposition a 3-0 win if a country is found guilty of fielding an ineligible player in a competitive international.
