The electoral commission last week excluded the 81-year-old politician, who is campaigning for a new opposition party, over a 2021 contempt of court conviction.
But in court papers seen by AFP, lawyers for Zuma and the party argued that the sentence did not disqualify him for it followed civil rather than criminal proceedings.
The electoral commission "had no valid reasons to violate the political rights of President Zuma," the papers said.
"(Zuma) was not an accused, he was not charged of an offence by a criminal court, he was not involved in any criminal trial proceedings."
South Africa is to hold general elections on May 29 in what is expected to be the most competitive vote since the advent of democracy in 1994.
The ruling African National Congress (ANC) is struggling in the polls and risks losing its parliamentary majority for the first time since the end of apartheid, amid a weak economy and allegations of corruption and mismanagement.
Among the groups that seek to capitalize on the ANC's weakness is Zuma's new uMkhonto we Sizwe (MK) party.
Named after the ANC's former armed wing during the anti-apartheid struggle, it looks poised to win a large share of the vote in the battleground region of KwaZulu-Natal — Zuma's home province — with some polls even putting it at 13 percent nationwide.
It largely relies on the considerable political clout still wielded by Zuma, who despite scandals and graft allegations is still largely popular particularly among the country's more than 10 million Zulus.
'Traitors'
The fourth president of democratic South Africa from 2009 to 2018, he has long been bitter about the way he was forced out of office under a cloud of corruption allegations.
Campaigning for MK in an attempt to relaunch his career, he has attacked members of the ANC, his former political home, as "traitors" and "sellouts."
But last week the electoral commission said he could not run in May for under the constitution "any person who was convicted of an offence and sentenced to more than 12 months imprisonment without the option of a fine" cannot stand in an election.
Zuma was sentenced to 15 months in jail in June 2021 after refusing to testify to a panel probing financial corruption and cronyism under his presidency.
He was freed on medical parole just two months into his term.
But his jailing sparked protests, riots and looting that left more than 350 dead in South Africa's worst violence since the advent of democracy.
An appeals court later ruled Zuma's release was illegally granted and ordered him back to jail.
On returning to a correctional center he immediately benefited from a remission of non-violent offenders approved by President Cyril Ramaphosa, his arch-rival and successor.
Tensions between the ANC and MK have flared in recent weeks.
The former has unsuccessfully tried to have the latter disqualified and has taken it to court to stop it from using the MK name, alleging intellectual property theft.
MK leader Visvin Reddy is due to appear before another court on Wednesday for allegedly inciting violence in a viral online video where he is heard saying massive riots would erupt if the MK was not allowed to run.
Reddy denies the charges.
The electoral court in Bloemfontein is expected to decide on Zuma's exclusion from the race next week.
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