Nationalist controlled Mid Ulster Council have carried a Sinn Féin motion strongly opposing the UK's decision to leave the European Union.
Councillor Phelim Gildernew said the majority of voters in the north of Ireland voted to remain in the Brexit referendum.
He claimed the uncertainty caused by the Brexit referendum result was already damaging trade and investment and causing currency fluctuations which are impacting on cross border business.
But DUP group leader Councillor Paul McLean expressed his "disappointment" that the motion had not been ruled out of order.
Speaking after the meeting, he said: "It's only a few months since it was previously debated in council.
"The decision has been taken that the UK of which Northern Ireland is an integral part is leaving the European Union.
"In case members have forgotten, we joined as one country and we leave as one country."
He described Councillor Gildernew's motion as "total nonsense."
He welcomed the initiative of those from the business sector, the community sector, farmer and individuals who have come together to form Border Communities Against Brexit to demand that the Irish and British Governments respect the North's remain vote.
"Recognising that it makes absolutely no sense to have one part of Ireland operating within the EU and another outside, this council will actively support the campaign by Border Communities Against Brexit or the North's remain vote to be respected," his motion read.