This came after Mandela made comments in July last year regarding the practice of Ukuthwala, the Tshwaranang Legal Advocacy Centre, the Commission for Gender Equality and the Rural Women's Movement said in a statement.
Ukuthwala is a practice where women, some as a young as 14-years-old, are abducted and forcefully married to older men.
Mandela is a grandson of former president Nelson Mandela.
According to the organisations, Mandela said the process of Ukuthwala had nothing to do with age and depended on whether the girl underwent the intonjane initiation, as arranged by her family.
"That is how culture works," he was quoted as saying at a rural development and land reform Parliamentary portfolio committee meeting.
"When you are going to discuss culture do not even try to bring in white notions as such an approach will turn things upside down," he said.
"Firstly, culture has no age. Age is something we learnt today because of our westernisation."
The three organisations met with Mandela on Thursday to discuss his comments.
Mandela was also asked to acknowledge section 3(1) of the Recognition of Customary Marriages Act which states that all prospective spouses must be over the age of 18 to enter into a customary marriage, the organisations said.
"On this basis the organisations asked honourable Mandela to also publicly condemn the abduction, kidnapping, assault and rape that currently accompany ukuthwala.
"These are all criminal offences that mitigate consent and are not in accordance with customary negotiations around marriage," they said.