Sinn Fein leader Michelle O'Neill has said the party is "building momentum" to ensure designated special status within the EU as the Brexit process has been triggered.
Theresa May has signed the letter that formally begins the UK's departure from the European Union.
The Prime Minister has sent the eight-page document to Donald Tusk, president of the European Council by courier to Brussels formally triggering Article 50.
The majority of voters in Northern Ireland backed Remain - 56% to 44%.
Speaking on Wednesday Michelle O'Neill said: "The Tory government don't have mandate here and they are dragging people of the north out of the EU against the democratically expressed wishes in a democratic vote.
"So we continue to make the case for special status.
"We are on the diplomatic offensive in Europe, using our MLAs, MPs, MEPs and making sure we are engaging with all those relevant in terms of negotiations - because the British Government won't dictate the terms it'll be the open member states.
"Clearly the Irish Government have a strong role and a strong negotiating role in terms of what will happen in weeks months and years ahead.
"Clearly we need to see special status and we are building momentum and that argument is resonating across Europe, we need to do a lot more of that and that's what we are committed to doing."
Michelle O'Neill lead fellow Sinn Fein MLAs in a protest held by Border Communities Against Brexit at Stormont on Wednesday afternoon.
She lead around 300 anti-Brexit protesters who set up a mock customs checkpoint at the gates of the estate to highlight concerns about a hardening of the Irish border when the UK leaves the EU.
They chanted "no borders, no barriers, no Brexit" as they made their way up Stormont's landmark main avenue.
DUP deputy leader Nigel Dodds spoke during Prime Minister's Questions in the House of Commons.
He said: "The Prime Minister has rightly been emphasising her determination to deliver for all constituent parts of the United Kingdom on this historic day.
"And whilst others are content to moan and whine we want to see that delivery happen and we are confident she will make that happen."
The Ulster Unionists campaigned for Remain but, since the result, the party has voiced support for the referendum result to be actioned.
UUP MP Danny Kinahan said: “Today as Article 50 is triggered by the Prime Minister, Sinn Fein are using Brexit as an excuse to agitate for separation from the United Kingdom.
“Instead their focus would be better placed working to ensure we achieve the best deal for all the people of Northern Ireland as part of the United Kingdom, for our farmers, our universities, our community & voluntary sector, our business community and all of society.
“This is not the time to be playing politics with the Union, or trying to create instability.
“I welcome Theresa May’s comments at Prime Minister’s Questions, that she will never be neutral on the Union, and cherishes Northern Ireland’s position within the United Kingdom.
“The United Kingdom has delivered so much for our citizens, it is vital that the people of Northern Ireland are shown how much our place within the Union is valued.
“I am glad that the Prime Minister has made that abundantly clear today.”
SDLP leader Colum Eastwood has described the triggering of Article 50 as an "act of savagery against our democracy".
He said: “Brexit is the single greatest threat to prosperity and stability facing this island since partition. People here recognised that and voted to remain in the European Union, to remain in the single market, to continue to enjoy the benefits and protections of EU membership.
“The British government’s Brexit juggernaut is about to smash through the fragile complexities of Irish politics. But worse than that, Theresa May is planning to trigger Article 50 while we face a political crisis in the North. Dragging us out of Europe against the will of our people and while we have no Executive isn’t just an affront to the principles of devolution, it’s an act of democratic savagery.
“The ignorance of this government must be met with strength from parties here. The referendum result is a mandate to take a stand against Theresa May’s tunnel vision and defend devolution. This challenge must unite us all.”
UUP MEP Jim Nicholson warned that the "constitutional integrity" of the UK must be protected and vowed to continue working for the best deal.
He said: "This is of course only the end of the beginning, and it is vital that we engage as much as possible both with Westminster and Brussels in ensuring that we get the best deal possible. I firmly believe that a bad deal for either side would ultimately be a bad deal for both sides.
“If we end up with ‘no deal’ that would be the worst possible outcome for everyone. Trading on World Trade Organisation (WTO) rules would mean significant tariff and non-tariff barriers to trade. For our agri-food and manufacturing sectors, this could be catastrophic.
He added: “The Government must also maintain a strong position regarding the constitutional integrity of the UK. We entered the European Union as one United Kingdom, and we will leave as one United Kingdom. Any measures that seek to diminish the Union, whether through internal UK borders, or by Nicola Sturgeon making yet another demand for a second referendum in Scotland - must be firmly rejected."
Meanwhile Retail NI Chief Executive Glyn Roberts said there were "real concerns for the future post Brexit".
He said: "Retail is Northern Ireland’s largest sector of the economy and our members on the border and many other areas and have real concerns for the future post Brexit.
“Triggering Article 50 is the start of a huge process of economic, social and political change for Northern Ireland and it remains to be seen if this change will be positive for our local economy. Certainly leaving the Single Market and Customs Union is neither positive for our retail sector or local economy as a whole.
“Northern Ireland’s retail sector needs a lot more certainty than just a vague aspiration about ‘no return to the borders of past’. The bottom line is that Brexit should not result in any barriers in trade and free movement across the border."
Mr Roberts urged Northern Ireland's parties to "redouble" their efforts in reaching a deal to form an Executive during Brexit negotiations.
He said: “It clearly is a major problem not having an Executive in place to argue our case in these vital Brexit negotiations. We urge all the political parties to redouble their efforts to secure agreement for a new administration.
“As part of these discussions the political parties should consider establishing an Assembly Brexit Committee to scrutinise the impact of the Brexit process on Northern Ireland and to take evidence from key sectors of Civic Society."