The Azanian People's Organisation (Azapo) said President Jacob Zuma was not beyond reproach on the matter of the child he fathered last year with a woman who was not his wife.
"His conduct is shameful not only to the nation but even to his family, especially his children who are now adults and look up to him for counsel," said spokesman David Lebethe in a statement on Thursday.
"It's about time for the man to know that he is not only accountable to his kinship and his organisation but to us all and that he is not beyond reproach."
Azapo said the matter was not wholly private as he was not an ordinary citizen.
On Wednesday Zuma confirmed a Sunday Times report that he had fathered a child with soccer boss Irvin Khoza's daughter Sonono, was correct.
He is married to three women and has a fiancee.
Critics suggested the birth of the child showed he was not practising the government's policies towards HIV/Aids prevention.