Church leaders have been meeting in New Zealand for their biennial synod where various motions were debated.
A majority group of members supported a motion to allow bishops to authorise blessings of same-sex relationships.
However, Anglican churches in the Pacific opted out of the debate by passing a resolution that they would not vote on the issue.
The Diocese of Polynesia released a statement saying the "constitutions and cultures" of its nations were reflected in its position on the issue.
The statement said the diocese honoured the church's work and understood the decision to allow same-same marriages was "located in the Maori and Pakeha context, within the laws and cultures of New Zealand".
But it said as far as the church was concerned, Pacific custom and protocol was against same-sex relationships.
The Pacific arm chose not to veto the motion, opening the door to the greater church's blessing of such relationships.
The Diocese of Polynesia stressed the church was still united and "the beauty of this decision is that no-one imposes on anyone... an authentic representation of our voyage together".