The Archbishop of Wales says making it illegal for the Church in Wales to offer same-sex marriages will be a "step too far".The UK government announced the Church in Wales and Church of England will be banned in law from offering gay marriages.
Other religious organisations will be able to "opt in" to holding ceremonies.
Culture Secretary Maria Miller said both organisations had "explicitly" stated strong opposition and would not be included.
The plans are due to be introduced before the next election, in 2015.
"I think that's a step too far," Dr Morgan told BBC Radio Wales.
Nurture
"This seems to exclude the possibility in the future."
He said although the Church in Wales was not currently contemplating offering same-sex marriages, he said the church believed in "nurturing family life".
He said the law had "curtailed" the church's freedom.
"There are those of us who think it ought to be a free choice and this increases the hurdles for people to pass," Dr Morgan said.
"It will have to get the legislation changed in parliament and change its cannon law - and it might be harder to change the law of the land than cannon law. In my personal opinion it's a great pity it's illegal for us not to even have the possibility to do it. It should be left for us to opt in or opt out."
Some religious groups, including Quakers, Unitarians and Liberal Judaism, are in favour.
Mrs Miller promised a "quadruple lock" to protect religious freedoms.
Mrs Miller said: "I am absolutely clear that no religious organisation will ever be forced to conduct marriages for same-sex couples, and I would not bring in a bill which would allow that. European law already puts religious freedoms beyond doubt, and we will go even further by bringing in an additional 'quadruple legal lock'. But it is also a key aspect of religious freedom that those bodies who want to opt in should be able to do so."
Prime Minister David Cameron said last week that he believed same-sex marriages should be allowed in churches - but only if there was a "100%" guarantee that no church, synagogue or mosque would be forced to hold one against their wishes.