The Archbishop, the Most Revd Justin Welby, invited Mr Tatchell to a meeting at Lambeth Palace after the campaigner had sent him a letter last month challenging his opposition to same-sex marriage.
Mr Tatchell described it afterwards as "the first-ever meeting between an international religious leader and a leading international gay-rights campaigner".
During the course of the day, Archbishop Welby also met six members of the LGBT Anglican Coalition, including the director of Changing Attitude England, the Revd Colin Coward.
In a statement issued after the meeting, Mr Tatchell said that the Archbishop had struck him "as a genuine, sincere, open-minded person, willing to listen and rethink his position".
Archbishop Welby was "clearly struggling to reconcile his support for loving, stable same-sex relationships with his opposition to same-sex marriage," Mr Tatchell said. "I got the impression that he wants to support gay equality, but feels bound by church tradition. . .The Archbishop told me: 'Gay people are not intrinsically different from straight people,' but there is an 'intrinsic difference in the nature of same-sex relationships', and this is a sufficient reason to deny gay couples the right to marry, even in civil ceremonies in register offices. When pressed to say why this 'intrinsic difference' justified banning same-sex marriage, he merely replied: 'They are just different.'"
Mr Tatchell went on: "The Archbishop did not accept that the ban
on same-sex civil marriage amounted to discrimination. He told me:
'I don't accept the word discrimination.'"Mr Tatchell also quoted Archbishop Welby as saying: "I am in favour of the state recognising same-sex relationships but not in favour of redefining marriage."
In Mr Tatchell's view, Archbishop Welby "supports a proposed amendment to open up civil partnerships to opposite-sex couples", although he does not quote Archbishop Welby directly as saying this.
Last month, Archbishop Welby told LBC Radio that the Marriage (Same Sex Couples) Bill, which is before Parliament, did "not include people equally. It's called 'equal marriage', but the proposals in the Bill don't do that".
However, it is not clear whether Archbishop Welby supports heterosexual civil partnerships in principle, or simply believes that the Bill is inconsistent in introducing civil marriage for gay couples but not civil partnerships for heterosexual couples.
In an interview with the Church Times last month, Archbishop Welby said: "It's perfectly clear . . . that you find relationships within the LGBT communities that are deeply loving, profoundly committed, and stable. . . But it remains absolutely clear that the Christian ideal for the upbringing of children is in a stable relationship between a man and a woman, committed in marriage to one another for life, and to the nurture and support of members of that family."
Lambeth Palace declined to comment on what was said between the two men. It was private meeting, a spokeswoman said.