The Institute for Accountability in Southern Africa, which has Archbishop Desmond Tutu as its patron, has written an open letter to ANC secretary general Gwede Mantashe to ask whether President Jacob Zuma is a "lawful and appropriate" candidate for the presidency in 2014.
The Institute is a non-profit group comprised of people from the legal profession and civil society, which has engaged on constitutional matters in the past.
On Thursday, it welcomed the "responsible and cautious" response the ANC had to the public protector's "Secure in Comfort" report on the president's home in Nkandla, but it cautioned that the party had done a great deal of talking and now needed to "walk the walk".
This was necessary to keep the country on the path of multiparty democracy under the rule of law, it said.
The findings of Madonsela's report and of the ministerial task team were enough to give "any reasonable, responsible and responsive decision maker cause for pause" regarding Zuma's presidency, it said.
The institute urged the ANC "to reconsider the implications of persisting with Jacob Zuma as your presidential candidate in the forthcoming elections and give serious attention to recalling him as presidential candidate if he does not opt to voluntarily resign".
The institute laid charges against the president last year, and cited the new charges laid by the Democratic Alliance (DA) and Economic Freedom Fighters (EFF) as making Zuma's continued presidency "inconsistent with the rule of law".
The president's "compromised moral and legal position" and the party's loyalty to him would have a detrimental affect on foreign investment and and overall confidence in the economy, it said. "Retaining JZ would also serve as a major distraction from the task of governing the country properly."
Zuma was "so compromised" and in "such an unmanageable conflict of interest position" that he was unable to fulfil his obligations to the country, it said. "He must therefore step down as president or be recalled by the party before the elections, or before Parliament or the Constitutional Court have to wade into the debate," it said.
They have asked for a response to the letter after the next meeting of the ANC's national executive council.