Former Sinn Fein leader Gerry Adams has made a fresh call for a referendum on a united Ireland.
The call comes just weeks after Irish Premier Leo Varakdar said such a poll would be "divisive" and a "bad idea".
Under the terms of the 1998 Good Friday Agreement, a referendum can be called if the Secretary of State believes a majority of people in Northern Ireland no longer want to remain part of the United Kingdom.
Former DUP leader Peter Robinson suggested in June that holding fixed generational polls on Irish unification as a way to stabilise politics in Northern Ireland.
However, the ex-First Minister said he felt very confident that citizens would choose to stay within the UK.
A recent opinion poll, conducted for former Conservative Party treasurer Lord Ashcroft, found that a majority of voters in Northern Ireland believe that the UK's vote to leave the EU had made unification with the Republic more likely in the foreseeable future.
It found a majority of just five points in Northern Ireland for staying in the UK, with 49% saying they would vote for the Union and 44% for Irish unification if a referendum was held now.
Speaking on Sunday at an annual republican commemoration in Mullaghban, Co Armagh, Mr Adams renewed his party's call for a referendum to be called.
The commemoration was for a number of republicans killed during the Troubles.
A stone was also unveiled in honour of former deputy First Minister Martin McGuinness, who officially opened the memorial garden in 2010.
Mr Adams condemned the DUP for their supply and confidence deal with the Conservative Party.
"The DUP have tied themselves to the English Tories; they embrace Brexit. They continue to deny citizens' rights enjoyed elsewhere on these islands. But that will all be sorted. Of that there is no doubt," he said.
"We can say with certainty that the DUP position is not sustainable. It is for them to come to terms with that.
"Everyone here knows that the Taoiseach's position on the North, the border and rights is a direct consequence of the strength of Sinn Fein. So we will persist and we will prevail.
"We also reject Mr Varadkar's suggestion that a referendum on Irish unity is not desirable at this time. He has a duty to uphold the Good Friday Agreement. He cannot cherry-pick it. So we will continue to look for a referendum and we will do our utmost to win that convincingly."
Mr Adams went on to urge other parties to speak out in favour of an Irish unity poll.
"This is not a task for Sinn Fein alone. All political parties and others who support the Good Friday Agreement and an end to partition should also campaign for this modest step forward," he said.
"How a shared Ireland, an agreed Ireland is created is another matter deserving of careful, generous and positive inclusivity. To begin with we need to understand that many unionists hold to their sense of identity as strongly as we do. So new thinking is needed by us all.
"We are a diverse people. That should be proudly proclaimed and not used to divide us. Ireland is an island - a society - in transition. The future is bright despite the dire threats of Brexit."