On Wednesday, the party filed a notice with the intention to approach the Supreme Court of Appeal.
Alternatively, it wanted a full bench of the South Gauteng High Court to hear an appeal against the whole order granted by Judge Colin Lamont on September 12.
Lamont found that singing "ayesaba amagwala" amounted to hate speech, and restrained the ANC from singing it at any of its public or private meetings.
Spokesperson Jackson Mthembu said on Wednesday that an appeal against the ruling would be in the interest of preserving the party's history and the struggle heritage of all liberation movements.
"Failure to appeal this ruling will result in a systematic erasing of the memory of our history."
The matter was taken to the Equality Court by civil rights group AfriForum after ANC Youth League president Julius Malema sang the song several times in public.
On Thursday, AfriForum CEO Kallie Kriel said it had already won two court cases with costs against Malema.
"AfriForum is prepared to do it a third and fourth time in the Appeals Court and Constitutional Court respectively."