Dr John Sentamu was reopening Southwell Minster when he was challenged over 'discrimination' against a gay priest who has married his same-sex partner.
Canon Jeremy Pemberton has been told he can no longer work in Nottinghamshire and has been stopped from taking other jobs as a priest because he entered a same-sex marriage.
He is now taking the Church of England to a tribunal.
Campaigner Peter Tatchell was waiting for the archbishop to arrive before questioning his position on the case.
But Dr Sentamu said he couldn't comment for legal reasons, since there is an active case.
According to the BBC, the archbishop told him: "Mr Tatchell, I have said that actually, at this particular point in time, while there is a legal case pending, anybody, you better than most, would know that actually I can't comment. Silence is the best articulation."
Speaking on BBC Radio Lincolnshire, Peter Tatchell said: "He can't perhaps comment about the individuality of that particular case, but he certainly could comment on the principle, which is that he has, in the past, supported legal discrimination against gay people.
"In particular, he opposed same-sex civil marriage in registry offices. And that's got nothing to do with the Church. It's a civil ceremony. That's what Jeremy and Laurence [Mr Pemberton's husband] undertook."