The Times, Ruth Gledhill reports and publishes the letters.
Gay partnerships pose the same ethical questions as those between a man and woman and the key issue for Christians is that they are faithful and lifelong, he believes.
Dr Williams is known to be personally liberal on the issue but the strength of his views, revealed in private correspondence shown to The Times, will astonish his critics.
In an exchange of letters with an evangelical Christian, written eight years ago when he was Archbishop of Wales, Dr Williams describes his belief that Biblical passages criticising homosexual sex are not aimed at people who are gay by nature.
Instead, he argues that scriptural prohibitions are addressed “to heterosexuals looking for sexual variety in their experience”.
He says: “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.”
Although written before he became Archbishop of Canterbury in 2002, Dr Williams describes his view in the letters as his “definitive conclusion” reached after 20 years of study and prayer. He refers to it as his “conviction”.
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