Atheist Ireland is voicing concern about the reinstatement of a cross at the summit of Carrauntoohill.
The organisation says it has no problem if it is on private property and has gone through the planning process.
However it objects to the cross being put up in a public space because it would not represent the whole community.
The cross on the county Kerry mountain was cut down last weekend in an incident which Atheist Ireland has condemned.
In an interview on Radio Kerry yesterday, Peter Hinchliffe, a member of Atheist Ireland, said:
"We don't condone people vandalising a cross or any other monument, wherever they are … [but] there needs to be a discussion [about what happens next].
"We really would like to see something that is reflective of the whole community, if the cross is to be replaced."
He was commenting following a letter published in yesterday'sIrish Times which read: "structures such as the cross have no place on top of such a beautiful mountain. It was out of place and a blot on the landscape.
"Before people go charging up to restore the cross I hope they remember to apply for planning permission as I am sure there are a lot of like minded people who would like to object."