Conservative group GAFCON says the American branch sat in on a meeting on polity and doctrine in Lusaka.
After the January 2016 Primates meeting it was decided that The Episcopal Church would not be allowed to "take part in decision making on any issues pertaining to doctrine or polity".
This was the Church's punishment for taking a view that was pro same sex marriage.
It is now claimed that this agreement was broken. However the Anglican Communion is said to have told GAFCON that there was no formal vote at the meeting so no rule was broken.
"This is sophistry," blasted GAFCON. "The Primates agreement in January was never limited to the narrow issue of the method of voting," the group added in a statement.
"Whether a meeting uses a consensus model, or a voice vote, or paper ballots, or electronic ballots is of no relevance. The Episcopal Church was not to take part in decision making on issues pertaining to polity or doctrine. They did."
Archbishop Peter Jensen, General Secretary of GAFCON, said: "The future of the Anglican Communion does not lie with manipulations, compromises, legal loopholes, or the presentation of half-truths; the future of our Communion lies in humble obedience to the truth of the Word of God written."
The Anglican Communion has been contacted for a comment.
