(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 cannot 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 shouldn'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."