Archbishop of Wales Dr Barry Morgan spoke at a meeting of the governing body in Llandudno on Wednesday.
The church tweeted "Archbishop of Wales offers a pastoral letter on same-sex relationships apologising unreservedly for prejudice within the church."
Last year, Dr Morgan said it would be "foolish" to bring forward a bill for same-sex marriages in church.
A statement released by the church said although it was not ready to allow or bless same-sex marriages, "the debate is not over".
It went on to apologise for "the persecution and mistreatment [gay people] have endured at the hands of the Church".
Dr Morgan also authorised prayers which can be said with same-sex couples following a celebration, but they fall short of a church blessing for civil partnerships and marriages.
However, Welsh Anglican bishops ruled out a change in the law to allow same-sex couples to get married in church.
Dr Morgan told the meeting there was concern the issue might tear the church apart.
Last year, an informal consultation showed a small majority of bishops, clergy and lay members in favour of change, but it was nowhere near the two thirds of the governing body needed.
Bishops will send a copy of the pastoral letter to all clergy, explaining their position.
It includes the apology to gay people for the way they have been treated and promises a "safe space" for them within the church.
The head of the Church in Wales has apologised "unreservedly" to gay couples for prejudice in the church.