President Goodluck Jonathan imposed the suspension last week following the embarrassing performance by the Super Eagles in the World Cup. The team were knocked out in the first round after failing to win a game.
Football's world governing body has given Nigeria until Monday evening to change its decision and escape being barred from all FIFA-related activities.
A Nigerian presidency source said on Friday the suspension would hold despite FIFA's threats.
However, a communique from an emergency NFF executive committee meeting on Saturday said: "We wish to passionately appeal to the president to reconsider the earlier decision."
The committee fired its top two leaders and offered an "unreserved apology" to the West African nation's 140 million citizens for the national team's failures.
"The leadership of the present NFF executive committee should be held responsible for the current crisis in Nigerian football," the committee said.
If the Nigerian government fails to heed FIFA's ultimatum, it risks being cut off from all FIFA activities, including junior and female competitions, and also losing FIFA funding.
A ban would also cut access to FIFA's development courses and stop the annual payment each member associations receives, cash that is much needed by Nigerian football.
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