The EFA have suspended Zaki after he was spotted insulting the referee of Zamalek's Egyptian League game against Baladeya, although the official did not include the incident in his report.
The decision has infuriated the Cairo giants' officials, who insisted they won't give up the club's rights whatever happens.
"We do always support national associations in order to contribute to the development of football in Egypt," Zamalek said in a statement late on Thursday.
"Nevertheless, we won't tolerate being targeted with some random decisions by football authorities in Egypt. We can react and defend our interests if we were forced to."
Zamalek did not clarify which measures could they take in future to oppose EFA decisions.
The men in white have also called on their fans to stay calm and leave the board acts in the best possible way to defend Zamalek interests.
EFA BIASED POLICY
Zamalek claim that their furious reaction is not down to Zaki's suspension but is due to the EFA's lenient stance towards similar incidents by other clubs.
They have also listed recent issues regarding Tunisian defender Wissem El-Abdi, former Zamalek midfielder Moataz Eno and newly-signed youngster Sherif Ahsraf which they believe were unfairly handled by the EFA.
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