Carl Niehaus, an ANC spokesman, said: "In general, the African National Congress, and many people in the ANC, including myself, have been very supportive of Jonathan Zapiro.
"We do believe that press freedom is important, but at certain times, one can unfortunately overstep the line and this was one of those cases."
The cartoon first appeared when Zuma was on trial for corruption. He was later acquitted.
Two years earlier, when he was deputy president of the ruling ANC, Zuma had been tried and acquitted of rape charges.
Zapiro says he has always been an ANC supporter, but now he is "going for" certain members he fears are acting wrongly.
"There are certain people like myself who have become disillusioned with the ANC, and who are going for them, or certain people within the ANC, really hard for doing things that we think are wrong," he told Al Jazeera.
"There is already a lawsuit against me, which has been around for a while, for cartoons I did a couple of years ago. It's sort of bubbling under, nothing is really happening.
"I would have thought that the intimidation attempt that that was, has been shown to be a bit of a failure in view of the fact that I just carried on, and so have most of the other people [Zuma] has sued."
|Zuma launched 14 lawsuits against the press after being acquitted of rape charges [AFP]
The ANC's Niehaus said: "I would say, and the ANC would support me, that press freedom is going hand in hand with responsible media reporting.
"I think many people understand that Mr Zapiro has all the free speech he wants in this country. This is not a repressive country. It is probably one of the freest countries in the world and we do have press freedom.
"What we are dealing with here is overstepping the mark and trying someone, who has been tried before, and continuing with insinuation and allegation that that person is a rapist."
When asked if Zapiro would rethink his cartoons, he said: "I am absolutely determined to keep doing what I do.
"Along with other critics in society, it's what I am here for, I will certainly do hard-hitting cartoons in the future."