An Auckland church was today sticking to its decision to continue displaying a controversial Christmas billboard despite criticism from the head of the Anglican diocese that the move was insensitive.

St Matthew-in-the City, an Anglican church, replaced a billboard that was vandalised yesterday and then stolen overnight with a copy depicting the same image of Joseph and Mary lying in bed.

The picture, which has attracted attention around the world, carries the caption "Poor Joseph, God was a hard act to follow".

St Matthew's church says the aim is to provoke conversation about spiritual matters by lampooning the literal Christian conception story and inviting people to think again about what a miracle is.

However, the Bishop of Auckland, the Rt Rev John Paterson, said he was "disappointed" that St Matthew's had chosen to go ahead with displaying the replica.

He said there were a multitude of other issues for a city and the wider church to focus on than a billboard.

"Discussion of theological perspectives and diversity is encouraged in a respectful way, but this approach is insensitive to communities across the Anglican Church as well as other denominations," he said.

"The season and story of Christmas is one that celebrates the life that is brought by Christ and that is the spirit of Christmas that I seek for the diocese and the city of Auckland."

But the Vicar of St Matthew's, Archdeacon Glynn Cardy, said having debate was always positive.

He said the idea behind the billboard was to move a debate that was inside the church to outside it "and certainly people in all sorts of places are talking about it".

He didn't doubt that some people had been offended by the billboard, but "the literalness of a male God impregnating Mary needs to be laughed at".

At the same time, "people can laugh at my perspective too".

As for the criticism of insensitivity, Mr Cardy said: "The Bishop has an opinion that is obviously different from ours."

He said the billboard would remain in place "at this stage".

"We just need to take it one day at a time," he said.

"If it's repeatedly vandalised, then there is a point where we say, well, actually, we've got better things to do."

The original picture was put up yesterday, but just over five hours later someone defaced it by smearing brown paint over it. Overnight, it disappeared.

St Matthew's marketing and communications manager the Rev Clay Nelson said the amount of reaction to the billboard had been "phenomenal".

The church had expected some comment in New Zealand, but messages were coming in from as far afield as Sweden, the Netherlands, Britain, Costa Rica and India.

"The emails are continuing to pour in and 90 per cent of them at this point are positive," Mr Nelson said.

He was trying to reply to all of them, whether positive or negative, but at the moment the emails were arriving faster than he could answer them.