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They were joined by the Freedom of Expression Institute.
"By taking this step, the president would be providing leadership on this critical issue," the FXI said in a statement.
"The FXI is prepared to take part in the litigation at the Constitutional Court should the president not heed the calls from various voices in the country to do so."
The institute said the passing of the bill was a regressive step that dampened the mood on this year's Freedom Day.
Catholic Archbishop of Cape Town Stephen Brislin said while there had been dramatic changes to the bill, it remained an "unsatisfactory piece of legislation".
"It lacks a full public interest defence and will thus make the fight against corruption more difficult," he said.
Further deliberation
"To fight corruption we need more openness, not more secrecy."
The SACBC wanted Zuma to send the bill to the Constitutional Court to avoid a protracted and costly court battle.
"On the eve of the celebration of Freedom Day, there is an opportunity for President Zuma to subject this bill to the Constitutional Court for further deliberation and so to protect the democracy which we all cherish," said Breslin.
Opposition parties and civil society organisations have indicated they intend launching a legal challenge should Zuma sign the contentious bill into law.
Parliament passed the proposed law on Thursday, after three years of debate and redrafting.
It adopted the bill by 189 votes to 74, with one abstention. – Sapa