( CNN ) -- Rifts within the Anglican Communion could widen after the archbishop of Canterbury , who has condemned the consecration of openly gay bishops , urged a diminished role Friday for the Episcopal Church . Earlier this month , a Los Angeles , California , diocese ordained the Rev . Mary Glasspool , the first openly gay bishop ordained in the church since 2004 , when Gene Robinson took his post in New Hampshire . The U.S. church has been criticized by conservative factions for openly gay ordinations . Archbishop of Canterbury Rowan Williams , the nominal head of Anglican Communion , shared his concern when Glasspool was consecrated , saying then that the move would further divide the 77 million-member worldwide denomination that includes the Episcopal Church in the United States . On Friday , he made an even stronger statement in a letter to the communion . `` Our Anglican fellowship continues to experience painful division , and the events of recent months have not brought us nearer to full reconciliation , '' Williams wrote . `` There are still things being done that the representative bodies of the Communion have repeatedly pleaded should not be done ; and this leads to recrimination , confusion and bitterness all round . `` It is clear that the official bodies of The Episcopal Church have felt in conscience that they can not go along with what has been asked of them by others , and the consecration of Canon Mary Glasspool on May 15 has been a clear sign of this . '' Williams does not have the power to issue edicts like the pope , but he issued a five-page statement suggesting that provinces ( such as the Episcopal Church ) or national and regional churches that have broken agreed-upon `` promises '' should step down from participating in interfaith dialogues . He said they should also relinquish decision-making powers in a committee that deals with questions of doctrine and authority . Following Robinson 's consecration , the communion leadership laid out three promises , or moratoria , according to the archbishop of Canterbury website : . -- No authorization of blessings services for same-sex unions . -- No consecrations of bishops living in same-sex relationships . -- No cross-border interventions ( no bishop authorizing any ministry within the diocese of another bishop without explicit permission ) . Glasspool has been in an open same-sex relationship for 19 years , a violation of the moratoria . Robinson also was in a same-sex relationship at the time of his consecration . Conservative Anglicans have long called for Williams to punish the Episcopal Church by not inviting the church to the Lambeth Conference , a global meeting of Anglican leaders held every decade . Williams did not go far enough in his rebuke , a spokesman for a conservative Anglican group said Friday . Robert Lundy of the American Anglican Council said the Episcopal Church should n't be involved in any decision-making bodies within the Anglican Communion so long as it continues to ordain openly gay bishops and violate biblical teachings . Williams ' statement only keeps the Episcopal Church off of certain committees within the communion , Lundy said . `` He [ Williams ] knows he has to do something because he 's under pressure from all sides , '' he said . `` But unfortunately , the step he 's taken in our view is not strong enough . '' Bishop Ian Douglas of the Episcopal Diocese of Connecticut called Williams ' statement `` significant '' but `` not as punitive as it might have been . '' He said it was an affirmation of the three moratoria , and he made clear that other churches , not just the U.S. Episcopal Church , will be affected for having broken promises as well . `` Many churches across the Anglican Communion because of conscience or their belief in what the holy spirit is up to in their local context have lived beyond the moratoria , '' Douglas said . `` While the moratoria are still before us , such actions do have some ramifications . ... If anything , I question the efficacy of the moratoria . '' He added , `` It 's another expression of how we 're trying to live with our differences with integrity and not alienate one another . I 'm still convinced there 's so much more that unites us . ''
The Episcopal Church in Los Angeles recently consecrated an openly gay bishop . Hide Caption 3 of 7 Photos:Same-sex marriage at the Supreme Court He urged a diminished role for the Episcopal Church for violating `` promises '' Conservatives say he did n't go far enough .