The DUP leader has dismissed as “project fear” reports of Cabinet concern about an Irish unity poll in the event of a no-deal Brexit.
Arlene Foster said the criteria for calling a referendum on Northern Ireland’s constitutional future had not been met.
Mrs Foster’s remarks came after the BBC quoted three unnamed Cabinet ministers talking about the increased likelihood of a poll if the UK leaves the European Union without a deal.
Under the terms of the 1998 Good Friday peace agreement, the incumbent secretary of state is obliged to call a vote on the constitutional issue if there is evidence of a change in public opinion in Northern Ireland in favour of Irish reunification.
Last month, it was reported that Northern Ireland Secretary Karen Bradley warned Cabinet colleagues that a poll on a united Ireland would be much more likely in the event of a no-deal Brexit.
Asked about the latest reported Cabinet concern on the matter, Mrs Foster said: “There are many people engaging in project fear at this point in time and we all have to recognise that.
The DUP leader added: “The Belfast (Good Friday) Agreement sets out the criteria for a border poll and it hasn’t been satisfied and therefore will not be called.”
Mrs Foster was asked about the issue after she met Taoiseach Leo Varadkar in Belfast.
Sinn Fein vice president Michelle O’Neill also met Mr Varadkar during his round of engagements with the Stormont parties.
Mrs O’Neill said she raised the issue of a referendum with the Irish premier.
“We have put the issue of a unity referendum to the Taoiseach, to the British Prime Minister on every occasion on which we would meet them,” she said.
“Remember the unity referendum is built into the Good Friday Agreement, it will be for the people of this island to decide the constitutional future.
“Clearly we want to see a deal, we do not want to see a crash out Brexit but if we do find ourselves in the scenario where there is a crash out Brexit, then the tools which the British Prime Minister and Taoiseach must look to are actually written into the Good Friday Agreement and that is the unity referendum.”
The republican leader said a referendum did not need to be “rancorous”.
“People often talk about fear, there is an absolutely massive opportunity for a new Ireland and agreed Ireland which we all can design and plan together,” she said.
Mrs O’Neill said there was also a need to clarify the “grey area” in the Good Friday Agreement around the criteria for calling a referendum, claiming it currently was left to the “whim” of the Secretary of State.