Anglican church leaders gathering in London for talks on homosexuality have described the start of discussions as constructive.
Dr Eames was optimistic after first day
At the end of the first day, the Archbishop of Armagh, the Most Rev Robin Eames, told journalists that attending church leaders from around the world were moving towards "a consensus situation."
The two-day emergency meeting at Lambeth Palace was arranged by the Archbishop of Canterbury, Rowan Williams, in response to the anger caused by the election of an openly gay bishop in the US.
The confirmation of Gene Robinson as bishop of New Hampshire enraged many traditionalist Anglicans, particularly in countries like Nigeria.
Conservative clergy there and elsewhere have threatened to leave the worldwide church if his appointment is not overturned.
News of the meeting's outcome was not expected until late on Thursday, but Dr Eames said: "I'm optimistic that the Anglican communion will emerge from this stronger than it has ever been.
"But I would also like to predict there will be greater honesty than we have had up to now."
Anglican leaders, known as primates, from
both sides of the debate have been meeting in London all
week to lobby for support.
'Policy change by stealth'
There is still fallout in the UK from the battle over moves to appoint an openly gay priest as Bishop of Reading this summer.
The row over the nomination of Canon Jeffrey John led to him withdrawing his candidacy amid fears his appointment would damage the "unity of the church".
His decision, in July, followed a campaign by evangelicals within the Church of England and the worldwide Anglican Communion.
Dr Williams, who is known for his liberal views on homosexuality, was accused of seeking to promote gay clergy in order to change the church's policy by stealth.
Also contributing to tensions within the church globally is the official church blessing of gay relationships by the Vancouver diocese in Canada.
Liberal leaders want individual branches of the church to have the freedom to decide their own destiny, allowing them to put their stance in line with more reformist views among some national congregations.
But a survey commissioned by BBC Radio 4's World This Weekend programme suggested that three-quarters of primates would not allow homosexuals to
become priests in their province.
Conservatives - such as Reverend Peter Akinola, of the Church of Nigeria - say there can be no compromise over homosexuality because, in their interpretation, it is clearly outlawed by the Bible.
The American Anglican Council, which represents U.S.
conservatives, contends the liberals are the ones who have
departed from the communion by accepting non-celibate gays.
The council's leaders will petition the
primates to "guide the realignment of Anglicanism in North
Dr Williams has readily admitted that a "messy" future is possible as the church battles to deal with issues such as gay blessings and gay clergy.
"I suspect that those who speak of new alignments and new patterns, of the weakening of territorial jurisdiction and the like, are seeing the situation pretty accurately," he told a journal earlier this year.
Traditionalist leaders, many of them living side by side with conservatively minded Muslims in developing countries, insist the US church reverse its policy or be suspended.
Many think the survival of the 70 million-strong worldwide church is at stake but so far there seems little scope for agreement.