Bishop Gene Robinson, who lives with his male partner, was consecrated two years ago as Bishop of New Hampshire in the United States. Many conservative clergy believe that the Bible explicitly condemns homosexuality and African church leaders say it is a strong cultural taboo in many of their areas.
The Lambeth Commission, established by the Dr Williams after Bishop Robinson's appointment, had urged conservatives and liberals to use their faith to find agreement over the issue. If they failed, the commission warned, the communion would fracture into a collection of disparate churches.
But leaders of the Anglican Communion in the United States have refused to apologise for the consecration or for adopting a unilateral position over gay clergy. Bishop Robinson has come under increasing pressure to resign but has steadfastly refused.
Lambeth Palace said the Dr Williams had met Bishop Robinson privately in London and discussed "the range of problems that have arisen". A spokesman described the encounter as "friendly but candid ... and came as part of the Archbishop's commitment to listening to the voices of all concerned in the challenges facing the Anglican Communion."
Last night Bishop Robinson was a guest speaker at the Oxford Union, and over the weekend he will attend events in London and Stockport to mark the 10th anniversary of Changing Attitude, the gay Christian pressure group.
The Rev Colin Coward, director of Changing Attitude, said Bishop Robinson's visit would encourage those who longed for the Church of England to unreservedly welcome lesbian and gay people. He said: "It is sad that he is unable to preside or preach at our anniversary service because of church rules which prohibit a partnered gay bishop from participating fully in an act of Christian worship in England.
"We are glad he is coming because it presents into our midst a partnered gay bishop who is legally and properly ordained by his church and makes visible and present what is already a reality. Here we have partnered gay bishops in England but they remain hidden to the wider church."
But other sections of the church were less enthusiastic about Bishop Robinson's visit. The Rev George Curry, chairman of the Church Society, an evangelical grouping within the Church of England, said Bishop Robinson was not worthy of the office he holds. "He has adopted and maintains a lifestyle that is totally contrary to the will of God as declared in the written word of God," he said.
"The real question is what are we doing about the people within the Church of England and within Anglicanism who are adopting views with regards to matters sexual which are contrary to the plain teaching of the word of God.
"We have a collective failure of leadership unfortunately - there may be individuals who are the exception to the rule - among the bishops of the Church of England to maintain and teach orthodoxy in as clear and as gracious a manner as they should do."
Bishop Robinson has been with his partner, Mark Andrew, for 15 years. He met him after his marriage failed. He has two grown-up daughters and two grandchildren.
Next month, gay and lesbian couples in Britain, including priests, will be able to register their civil partnerships.