The spiritual head of the Anglican Church has warned that sharp divisions over the ordination of gay clergy in North America could become permanent.
Anglicans are making space for their members, Williams said
Archbishop of Canterbury Rowan Williams spoke after the Church's US and Canadian branches were asked to leave a key Church council for three years.
"Any lasting solution will require people somewhere along the line to say, 'Yes, we were wrong'," he said.
The head of the US branch has again defended ordaining a gay bishop.
Frank Griswold, Presiding Bishop of the American Church, told the BBC that the ordination of Gene Robinson in New Hampshire had been "right and proper".
"I continue to feel that way about the decision and the action - recognising that it is extremely problematic and difficult in many parts of the world," he said.
At the same time, the Church in the US welcomed the withdrawal as a chance to "move forward together".
The BBC's religious affairs correspondent, Jane Little, says there appears to be little hope for reconciliation and it looks like the world's third-largest Christian body is heading for a permanent split.
Anglican Church primates, or leaders, from all over the world spent a week debating the gay issue when they met in Newry, Northern Ireland.
The North American branches have been asked to leave from the Anglican Consultative Council (ACC) until 2008.
Anglicans have been divided since Bishop Robinson's ordination in 2003 while the Anglican Church of Canada upset traditionalists by blessing same-sex unions.
On Thursday, the primates issued a statement saying the "standard of Christian teaching on matters of human sexuality" had been "seriously undermined by the recent developments in North America".
Dr Williams told reporters on Friday that the issue was "not going to go away".
"We still face the possibility of division, of course we do... Any lasting solution will require people somewhere along the line to say, 'Yes, we were wrong'."
However, he noted an "impressive" willingness within the Anglican community to find a way forward without division.
The point of the withdrawal, he said, was to "make some space" for all parties to consider their positions.
Archbishop Andrew Hutchison, primate of the Anglican Church of Canada, said the final statement was "not a perfect document" but sought to provide "a way forward in spite of the differences that exist concerning the subject of homosexuality".
The leader of Australia's Anglican Church, Archbishop of Perth Peter Carnley, insisted Anglican leaders had "no intention" of watering down the worldwide communion.
He ruled out suggestions the 38-nation Anglican Communion might become "a kind of loose-knit federation".
"We are theologically grounded in the communion of God the Holy Trinity and that's what we want to maintain," he said.
The homosexuality debate has pitted traditionalists, notably from the African branches of the Anglican community, against more liberal elements.
The primates have suggested a special hearing in June to allow the US and Canadian branches to explain their views on homosexuality.