Prime Minister Theresa May has said the circumstances for which to call a border poll don't exist as most people in Northern Ireland don't want one.
She was reacting after a Times report which claimed she expressed doubt Northern Ireland would remain within the union after such a poll amid the mounting issues surrounding Brexit.
The Good Friday Agreement states there should be a border poll if the Secretary of State feels the majority would vote for unification.
Asked if the she was confident unionists would win an Irish border poll if it came to it, the Prime Minister’s official spokesperson said: “The Government steadfastly supports the Belfast agreement.
"It remains the Northern Ireland Secretary’s view that a majority of people in Northern Ireland continue to support the current political settlement, and that the circumstances requiring a border poll are not satisfied.”
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On Monday the Prime Minister called many of her backbench MPs to Downing Street to outline options for the Irish border in a bid to unite her party.
The Times reports that during an exchange with Jacob Rees-Mogg in which he suggested maintaining an open border Mrs May countered that the EU could impose infrastructure to protect the integrity of the single market.
Sources said the Brexiteer told Mrs May he had "no doubt" Northern Ireland would remain within the UK after any border poll.
Apparently Mrs May responded: "I would not be as confident as you. That’s not a risk I’m prepared to take. We cannot be confident on the politics of that situation, on how it plays out."
A Tory MP said Mrs May "slapped him down hard".
"She got him on facts.
"She was absolutely firm and passionate about the Irish position. I got a sense she realises what really matters," the MP told the Times.