SINN Féin and the DUP have clashed in the European Parliament over the Brexit vote.
The DUP's Diane Dodds told the EU elected members that the people's verdict could not be re-written but the EU and the UK could work closely together.
But Sinn Féin's Martina Anderson pleaded for Northern Ireland to be allowed to stay in the EU.
"If English votes drag us out of the EU, that would be like Britannia waives the rules," she said.
In an impassioned plea to the parliament on Tuesday, she said that she did not feel bound by the UK vote and stood by the people of Northern Ireland who, like Scotland, voted to remain in Thursday's referendum.
"There was a democratic vote – we voted to remain," Ms Anderson said.
"I tell you that the last thing that the people of Ireland need is an EU border with 27 member states stuck right in the middle of it."
Ms Anderson appealed to members to continue to support the peace process: "The EU has supported our peace process. I ask you to continue to do that.
"MEPs like Diane Dodds and Marine Le Pen would say that we in the north of Ireland are bound by a UK vote. We say we are not.
"Like the previous MEP (Alyn) Smith, we ask you to respect our vote. We stand by the vote of the people from the north of Ireland, just like Scotland, which voted Remain.
"We accept, we respect and we will defend the wishes of the people of the north of Ireland."
But Mrs Dodds told members of the parliament in Brussels that it was time to look forward to a new era after they had turned a deaf ear to the wishes of the British people.
"For years, the people of the United Kingdom have been trying to tell you of their frustrations and concerns about the EU," she said.
"You turned a deaf ear, but today, you are listening.
"Our nation has not turned its back on Europe – we are not inward-thinking.
"We have for a long time sought a new relationship with our European allies – a positive relationship based on self-governance, free trade and co-operation – to make our world more secure and more prosperous.
"That doesn't make us any less European and it doesn't make us any less optimistic.
"History proves that an independent United Kingdom not only has the strength of character to succeed for ourselves, but also the inherent humanity to defend the freedoms of our neighbours."
Both MEPs however said they will not turn their backs on Europe after the Britain's EU referendum.
The north is represented in Europe by three MEPs – Ms Anderson, Mrs Dodds and Jim Nicholson of the UUP, the longest-serving of the three.
Meanwhile a Scottish nationalist MEP has received a standing ovation at the European Parliament following his demand for Scotland to remain within the EU family of nations.
SNP MEP Alyn Smith was speaking in an emergency debate at the European Parliament in the wake of the UK vote to leave the European Union on June 23.
He reminded MEPs that Scotland voted to Remain, demanded that status "be respected" and begged parliamentarians from around Europe: "Do not let Scotland down."
SNP leader Nicola Sturgeon is understood to be heading to Brussels on Wednesday for talks with senior figures about protecting Scotland's place in the EU.
She has pledged to explore all options - up to and including another Scottish independence referendum.
Addressing the meeting of the Parliament, Mr Smith said: "I want my country to be internationalist, co-operative, ecological, fair, European - and the people of Scotland, along with the people of Northern Ireland and the people of London and lots and lots of people in Wales and England, also voted to Remain within our family of nations.
"I demand that that status and that esprit europeen be respected.
"Colleagues, there are a lot of things to be negotiated and we will need cool heads and warm hearts, but please remember this: Scotland did not let you down. Please, I beg you, cher colleagues, do not let Scotland down now."
