In the House of Commons the DUP's deputy leader, Nigel Dodds, has accused the Taoiseach of wanting to suck Northern Ireland back into the institutions of the European Union while the rest of the UK leaves.
The MP for North Belfast raised the issue in the House of Commons in London and said he welcomed the British government's commitment to the economic and constitutional integrity of the United Kingdom.
During Northern Ireland Questions, Mr Dodds said that when Leo Varadkar talks about not leaving Northern Ireland behind, what he means is sucking Northern Ireland into the institutions of the EU, "which would be economically disastrous for all of our citizens," he said.
In response, the junior minister in the Northern Ireland office, Shailesh Vara, said the British Prime Minister had made it absolutely clear that neither she, nor any other prime minister, would ever compromise the economic and constitutional integrity of the UK.
He said that means Northern Ireland is very much a full part of the rest of the UK, along with Scotland, Wales and England, and there was no question whatsoever of having a border in the Irish Sea.
Mr Dodds also said: "The vast bulk of Northern Ireland's external sales go to the Great Britain market. Indeed, more goes to Great Britain than to the Republic of Ireland, European Union and rest of the world combined. Anyone advocating that Northern Ireland should remain in the customs union, whilst the rest of the UK leaves would inflict economic misery on everyone in Northern Ireland."