The first and deputy first ministers have said there was widespread support at a meeting in Downing Street for their argument that Northern Ireland is facing "unique circumstances".
Their comments relate to Northern Ireland's position in the wake of the UK's decision to leave the EU.
Both ministers emphasised to the leaders of the other devolved administrations that Northern Ireland was the only region with a land border with an EU state.
Arlene Foster and Martin McGuinness made the comments at a Joint Ministerial Committee meeting chaired by Theresa May on Monday.
They told the prime minister Northern Ireland must be "fully represented" in the UK's negotiations to leave the European Union.
Both the First and Deputy First Ministers said it was imperative Northern Ireland remained involved in the Brexit process on a "high level" and on a "continuing basis".
Mrs May attempted to allay their concerns by telling the devolved administrations she would strike a bespoke Brexit deal that works for the whole of the UK.
Mrs May said that how the UK leaves the EU should not be seen as a series of binary choices and will instead amount to a bespoke agreement for the UK.
"We have important work to do for the UK in terms of negotiating a smooth exit from the EU and getting the best possible deal for the whole of the UK," she said.
"The UK has chosen to leave the EU and we're going to make a success of it," she added.
The Secretary of State for Northern Ireland James Brokenshire failed to provide reassurances that EU citizens would not be able to exploit a so-called "soft border" to gain access to the UK through Ireland.
He told BBC Radio 4's World At One: "It is precisely these issues of policy that are being debated to reach an agreement.
"But no decisions have been taken as yet," he said.
"It is why the work we have with the Republic as well as the Executive matters so much in relation to the border."