First Minister Rhodri Morgan is under fire for joking about Democratic Unionist Party leader Ian Paisley in front of Wales and Northern Ireland Secretary Peter Hain and Tony Blair.
Some opposition politicians think Rhodri Morgan should apologise
Mr Morgan said Mr Paisley converted to Catholicism before dying because he thought it better to lose a Catholic than a Protestant.
The DUP said Dr Paisley would not be commenting about the "poor taste" joke.
Mr Morgan's spokeswoman said no offence had been intended.
Playing down the incident, she added: "The joke used by the first minister is an old one, which has been doing the rounds for a long time.
"He certainly did not intend it to cause offence."
Mr Morgan made the quip at a dinner on the eve of the Welsh Labour conference in the presence of Wales and Northern Ireland Secretary Peter Hain and PM Tony Blair.
A DUP spokesman said: "It's not a remark one would expect from a first minister from any part of the United Kingdom. "We are involved in more serious activity and we would trust that the Welsh first minister would be more careful with his language and not been so offensive."
A spokesman for Peter Hain at the Northern Ireland Office said: "Peter thought that the joke was inappropriate and in poor taste and he knows that Rhodri Morgan now recognises that."
The Conservatives described the joke as "tasteless" and "hurtful" and called on Mr Morgan to apologise.
But Ian Paisley Junior, Dr Paisley's son, has laughed at the joke.
On hearing reaction to the remark, he said that politicians should be a "born with an extra chromosome" to give them thicker skin.