In a letter the bishops of the Church said it would not be wise to bring the plans before the governing body because there was not a clear majority in favour of it.
The bishops apologised for past treatment of LGBT people and promised to ensure they are "fully affirmed as equal disciples".
Debates on whether to have same sex weddings in churches would continue, the letter added.
It accepted that "a majority of members supported change" but stated that "there was certainly no consensus, and any move to introduce changes in canon law would not meet the required two thirds majority of Governing Body".
A series of prayers which may be said with a couple following the celebration of a civil partnership or civil marriage have also been published.
The Archbishop of Wales, Dr Barry Morgan, said: "We are not ready, as a Church, to take the step of authorising same-sex marriage.
"There is no point in bringing forward a Bill for it to fail. That I know will be a disappointment to those who voted for change and will be a deep disappointment to same sex couples within the Church in Wales who long for the opportunity to make their vows in one of our churches.
"We, as bishops, feel that this is the right thing to do at this time. I realise that some people will regard these prayers as too little too late and others will regard them as a step too far.
"No one is compelled to use them, but they are provided for those who would like to do so. These prayers do not constitute a service of blessing."