The call comes ahead of the motion of no confidence debate in Parliament on Tuesday.
The family also expressed their wish that the biggest ANC region in the Western Cape no longer be named after the stalwart.
The region was disbanded by the Provincial Executive Committee for insubordination a few weeks ago.
Speaking to the Weekend Argus, Omar’s sister Latifa Omar said: “We are calling for President Zuma to step down because we do not believe that he is a fit person to be President of the ANC and the country.
“There are just too many allegations of corruption, so many untested charges that are yet to go before the courts.”
She says although the family was not consulted when the Dullah Omar region was named, they didn’t mind “because at the time the ANC had not deteriorated to the state that it has now”.
“What it stands for now contradicts the values that my brother and the ANC of Nelson Mandela and Walter Sisulu and the others stood for,” she says.
However, she says the family remains staunch ANC supporters.
ANC Secretary General, Faiez Jacobs, said they would be engaging with the Omar family to discuss their concerns.