Tensions within the Anglican Communion have been heightened by the election of a woman as head of its US branch.
Katharine Jefferts Schori, a liberal who supports same-sex unions, won a vote among her fellow bishops at an Episcopal Church convention on Sunday.
Archbishop of Canterbury Rowan Williams praised her, but warned the move could highlight "continuing issues" between branches of the worldwide communion.
Most have resisted elevating women bishops and oppose homosexuality.
Bishop Schori's election was hailed by many US Episcopalians as a victory for women.
However, it deepens the split between liberals and conservatives among the world's 77-million-strong Anglican Communion, analysts say.
KATHARINE JEFFERTS SCHORI
Church of England Bishop of Rochester Michael Nazir-Ali said schism was now a serious risk.
"Nobody wants a split but if you think you have virtually two religions in a single Church, something has got to give sometime," he told The Daily Telegraph.
Prayer
Church Times editor Paul Handley told Reuters news agency: "Having a woman primate is an exciting complication.
"The problem is her views. She is quite permissive towards local churches giving blessing to same-sex couples and she supported the ordination of Robinson."
In his statement on Monday, Dr Williams said Schori was taking up "a deeply demanding position at a critical time".
He added: "We are continuing to pray for the general convention of the Episcopal Church as it confronts a series of exceptionally difficult choices."
The convention in Ohio is under pressure to "repent" of its decision to ordain Gene Robinson, to ban future openly gay bishops and to end the blessing of same-sex unions in church services.
A compromise is being considered to offer repentance only for the effect on the wider Church.
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