Brexit: Martin McGuinness 'to press case' for NI's EU status
Martin McGuinness has said he does not accept Northern Ireland cannot maintain any kind of special status within the EU after the UK withdraws from it.
Earlier, Secretary of State Theresa Villiers said EU rules do not permit part of a country remaining within the European Union.
In Northern Ireland, the majority of voters (56%) voted for the UK to stay in the EU in last week's referendum.
But overall, the UK voted to give up its EU membership by 52% to 48%.
"I believe that the mandate that we got during the course of the referendum to remain puts us in a very special place," Mr McGuinness, the deputy first minister, said after meeting Irish Foreign Affairs Minister Charlie Flanagan .
"It's quite clear that Scotland will make that same case.
"Theresa (Villiers) has to understand, as far as we in Sinn Féin are concerned, this is not a done deal, there is still a lot to be played for in the time ahead and we will be asserting the rights of those people who voted to remain in Europe."
Earlier, speaking ahead of a British-Irish meeting to discuss the political way ahead after the referendum result, Ms Villiers said: "The EU rules are very clear - membership is at member state level, it's a national question."
She added: "This decision has been made - the people of the UK have voted to leave the EU.
Ms Villiers hosted Mr Flanagan to discuss the fallout from the EU referendum result.
Mr Flanagan said the meeting was a welcome opportunity to discuss the referendum result.
"I reiterated the government's commitment to the stability and prosperity of Northern Ireland and how we will seek to highlight the need for the EU to take account of the Northern Ireland dimension in upcoming negotiations in order to minimise any negative impact that may arise as a result," he said.
Northern Ireland Executive ministers were also meeting to consider the implications of Brexit and the potential impact on their government departments.
The politicians meeting at Stormont are deeply divided about the issue.
Both Sinn Féin and the SDLP have said they do not want to be "dragged out of the EU" on the basis of English votes.
But First Minister Arlene Foster and and her Democratic Unionist Party campaigned for a Leave vote
She said: "The campaign is over, the decision has been taken, and now it is our job to go ahead and to represent the people of Northern Ireland in terms of the negotiations that are going to take place now.
"That's certainly my focus, to get the best deal for Northern Ireland in terms of the Brexit from the European Union," she said.
Scotland First Minister Nicola Sturgeon travelled to Brussels on Wednesday to seek to protect her region's relationship with the EU.
Gibraltar, which, like Scotland and Northern Ireland, voted to remain in the EU, has signalled it wishes to explore its options..