In a statement issued on behalf of the GAFCON Primates Council, Archbishop Eliud Wabukala said the move would create further confusion about Anglican moral teaching.
He also stated that it would make the restoration of unity to the worldwide Anglican Communion "an even greater challenge".
Dr Wabukala called upon the Church to promote marriage "without compromise and ambiguity".
"It is a great sadness that before the New Year has hardly begun, the life of the Anglican Communion has yet again been clouded by compromise with the secular preoccupations of the West," he said.
The Church of England announced last week that clergy in civil partnerships could be considered for the episcopate on the condition that they remain celibate.
However, Dr Wabukala said the requirement of celibacy was "clearly unworkable".
"It is common knowledge that active homosexuality on the part of Church of England clergy is invariably overlooked and in such circumstances it is very difficult to imagine anyone being brought to book," he said.
"However, the heart of the matter is not enforceability, but that bishops have a particular responsibility to be examples of godly living. It cannot be right that they are able to enter into legally recognised relationships which institutionalise and condone behaviour that is completely contrary to the clear and historic teaching of Scripture, as reaffirmed for Anglicans by the 1998 Lambeth Conference in its Resolution 1.10."
He added: "The weight of this moral teaching cannot be supported by a flimsy proviso."