The African National Congress (ANC) said the uMkhonto we Sizwe (MK) name and logo were similar to those of the now disbanded apartheid-era military wing of the ANC and that this could deceive or confuse voters.
The court battle is the latest move amid political tensions in the southern African country headed to general elections on May 29.
The long-dominant ANC is expected to lose ground and is fighting to hold a majority.
Zuma, 81, who was forced out of office in 2018 under a cloud of corruption allegations, is campaigning for MK in an attempt to relaunch his career and weaken his former party, the ANC.
"Mr. Zuma and his collaborators... have registered a political party appropriating the uMkhonto we Sizwe logo and related symbols unlawfully" the ANC said in a statement after filing the urgent court application.
The court move is to prevent "the Zuma party from passing itself off as being connected with the ANC by the use of the name uMkhonto we Sizwe" which means Spear of the Nation in Zulu, the ruling party said.
The ANC, in government since the advent of democracy, has also demanded that the MK be banned from using the logo which depicts a fighter with a spear and shield wearing traditional African attire— almost identical to that of the former armed wing.
A court decision is expected to be announced in the coming days.
On Tuesday, a court rejected an initial complaint by the ANC, which said the MK was registered unlawfully, allowing the small radical party to stand in the election.
In power for three decades, the ANC is bleeding support amid a weak economy and allegations of corruption and mismanagement.
"The movement created by our forefathers the ANC has been out of line lately," Zuma told supporters outside the court.
"We need to win by a landslide, we need to win with two-thirds majority" he said.
Struggling in the polls, the ANC risks losing its parliamentary majority for the first time since 1994 which may force it to form a coalition.
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