Carmarthenshire council voted to drop the English stream at Ysgol Llangennech, near Llanelli.
Michael Jones, a co-ordinator for Parents for Welsh Medium Education, said the decision should be accepted.
"If they do not like the Welsh language, can I suggest that that border is over there," he said.
"And they can cross the border," he added.
The removal of the English medium stream at the school has been an attempt to increase Welsh-language provision after a fall in the number of Welsh speakers; however English will still be taught as a subject.
Mr Jones told Welsh language news programme Newyddion 9: "If they do not want to be in a country where Welsh is spoken, well go somewhere else.
"But, if not, accept the fact there are two languages in Wales. I'm not saying that because they are English speakers to leave Wales.
"But I do say that if they cannot stand and hear the Welsh language, they better go somewhere else."
The move follows a bitter battle within the community over the issue. At the Carmarthenshire council vote vote - 38 councillors were in favour of the proposal and 20 against.
On Friday, Parents for Welsh Medium Education, known as RhAG, distanced itself from the remarks made by its co-ordinator Michael Jones and demanded an apology from the BBC.
The statement said: "RhAG (Parents for Welsh Medium Education) is demanding an apology from the BBC for today's news items involving Welsh medium education.
"The items claim that RhAG wants people who don't wish Welsh medium education to move across the border.
"RhAG has never expressed this, and RhAG would never profess such an idea.
"RhAG's aim is for Welsh medium education to be available to all who wish their children to be fully bilingual."
Parents unhappy their children's school has been changed to a Welsh medium primary should move over the border, a leading campaigner has said.