Campaigners against more law-making powers for the assembly have criticised a Catholic message supporting a Yes vote.
Catholic leaders in Wales say they would welcome strengthening the "democratic legitimacy" of the assembly.
But No campaigners True Wales called it an "inappropriate" endorsement of the Yes argument.
The Yes campaign welcomed the sentiments of the message.
It was circulated to be read at the end of masses on Sunday.
It said that having a Welsh assembly was in line with the Catholic principle of subsidiarity, meaning that that decisions should be taken as closely as possible to the citizen.
Voters go to the polls on Thursday in the referendum on whether the assembly should have direct law-making powers over devolved policy fields.
"We, as the current leaders of the Welsh Catholic Dioceses, are not now recommending how to vote in the referendum," read the message.
"However, we broadly support the principle of improving the functioning of the assembly and point out that this would be in line with the principle of subsidiarity found in Catholic social teaching.
"We would welcome measures to improve the assembly's decision-making process.
"We would also welcome a strengthening of the democratic legitimacy of the national assembly and any measures to increase the accountability of the politicians elected to the assembly."
The statement was signed by Bishop of Wrexham, the Right Reverend Edwin Regan, Bishop of Menevia, the Right Reverend Tom Burns and Monsignor Robert Reardon, diocesan administrator for the Archdiocese of Cardiff.
In response, Rachel Banner of True Wales, the main group campaigning for a No vote, told BBC Wales: "I think it's inappropriate they are endorsing the Yes campaign.
"I think that the churches are expressing too much of a view.
"If the current devolution settlement we had respected subsidiarity then there would be something in that. But I don't think we've got proper devolution at the moment and I think the bishops are out of line with the churchgoing public.
"The sort of devolution we are heading towards is more about Whitehall down the bay than subsidiarity."
Monsignor Reardon defended the Catholic statement: "We would never tell people how to vote but we are pointing out that devolution is compatible with the church's social teaching.
"We are just urging people to vote because that is the responsibility of a good citizen."
A spokesman for the Yes for Wales campaign applauded the Catholic bishops for urging people to vote in Thursday's referendum.
"We agree that bringing decision making closer to people is a good principle that should shape how people vote.
"Churches, charities, community groups, and other representative bodies like the Muslim Council for Wales, all advocate a Yes vote, but equally importantly they are asking people to think about the issues and turn out to vote.
"We are pleased the Catholic church is also encouraging people to take social responsibility and be part of that same big decision."