He was booed when he was giving a speech in Pretoria on Thursday as he left the council chambers where the National House of Traditional Leaders held a debate.
The South African Council of Churches (SACC) General Secretary Bishop Malusi Mpumlwana said that the group had met with African National Congress (ANC) leaders to discuss the issue.
Bishop Malusi Mpumlwana said: "We were met by the leadership of the ANC.
"We were disappointed that the President and Deputy President Cyril Ramaphosa were not available during the meeting... We asked for the president to resign," he said to Catholic World News.
He said that many leaders were struggling with the decision but that religious leaders felt that the president needed to stand down.
Mr Zuma has been nicknamed the 'Teflon president' after he has been able to last scandal
Earlier in the month South Africa's top court ruled that the president failed to uphold the constitution after he ignored an order from the state to repay around £11 million of government funds, used to upgrade his home.
The court also ruled that parliament, dominated by African National Congress, failed in its obligations by not holding Mr Zuma properly to account.
He also survived an attempt to impeach him after the ANC party gave him its backing last week.
