Dr Williams allegedly affirmed his liberal position on homosexuality in a leaked exchange of letters between 2000 and 2001 with Deborah Pitt, an evangelical living in his former archdiocese in south Wales.
According to media reports, Dr Williams asserts in the letters his belief that parts of the Bible relating to homosexuality were addressed "to heterosexuals looking for sexual variety in their experience" rather than gay people in a relationship.
"I concluded that an active sexual relationship between two people of the same sex might therefore reflect the love of God in a way comparable to marriage, if and only if it had about it the same character of absolute covenanted faithfulness," one letter was quoted as saying.
Dr Williams as a theologian is liberal on the issue of homosexuality but adopts a more conservative position as spiritual leader of the Anglican Communion, which officially regards homosexuality as incompatible with Scripture.
The Archbishop's comments come just days after the conclusion of the once-in-a-decade Lambeth Conference, which reaffirmed the Anglican Communion's official line on homosexuality.
Bishops at the conference, which ended on Sunday, called for an immediate halt to same-sex consecrations and blessings, and the suspension of cross-border interventions.
Dr Williams said at the end of the conference that the Anglican Communion would be in "grave peril" if member churches failed to observe the moratoria.
The churches at the heart of the row are the US Episcopal Church, which ordained the openly gay Gene Robinson as Bishop of New Hampshire in 2003, and the Anglican Church of Canada, where a number of dioceses offer blessings for same-sex unions.
Canadian Bishop Don Harvey told Reuters news agency that he did not believe cross border interventions would end until the Canadian Church put a stop to same-sex blessings. He also rejected the idea of suspending such blessings in new parishes whilst allowing existing ones to continue offering them.
"That will be completely unacceptable to us. That will not be an answer," he said. "I think the Communion is already in grave peril…It's in even greater peril if the same-sex blessings continue."