Churches and religious organisations have expressed disappointment at the court ruling approving same-sex marriages.
The Reverend Molefi Tsele, general secretary of the South African Council of Churches (SACC), said the SACC would have to live with the decision as it was based on the constitution.
The ruling was "not in line" with the traditions and teachings of member churches.
'We have to live with the difficulty'
"It is a situation that is still foreign to the core teachings of our member churches," Tsele said.
"We, however, respect the fact that it is based on our constitution, to which we ascribe, and it is designed to protect the rights of people irrespective of their sexuality. We have to live with the difficulty."
The Southern African Catholic Bishops' Conference said the ruling contradicted the law of God.
Its president, Cardinal Wilfrid Napier, said: "It shows that majority opinions are not always the correct ones. It also shows man-made laws can be contradictory to God's.
"The Church believes that marriage is between man and woman and is for bringing children into the world.
'Man-made laws can be contradictory to God's'
"Anything which is not in line with those basics is contradictory to our teachings," he said.
The ChristianView Network said the decision was very disappointing and went against the views of most South Africans.
Its director, Philip Rosenthal, called the ruling "one of the most extreme decisions in South African legal history".
"If the Constitutional Court supports the ruling, they might instruct parliament to change the laws relating to marriage. Nevertheless, parliament might not necessarily comply."
He added that "the court decision violates moral values, democracy and the separation of powers in government".
Rosenthal urged South Africans to resist this "judicial tyranny" and uphold the sanctity of marriage.
Most political parties welcomed the ruling, but there was vociferous opposition from the African Christian Democratic Party, which called for a referendum on the issue.