DUP leader Arlene Foster has said that she wants a solution to Brexit that does not affect Northern Ireland's constitutional position.
Mrs Foster was speaking to reporters before she addressed the Dublin City Chamber of Commerce.
She also met with Taoiseach (Irish Prime Minister) Leo Varadkar in Government Buildings after her address.
They discussed Brexit and the need for restoration of devolution.
Asked if NI-specific solutions would not affect the current constitutional position of Northern Ireland, Mrs Foster said she wants a recognition that Northern Ireland is in the United Kingdom.
"What I want to see is Northern Ireland firmly being with the rest of Great Britain," she said.
"What we want to see happening is a recognition that we are on an island, we recognise that and we recognise the unique history and geography," she said.
"But we also have to recognise that we're in the UK and sometimes I think people forget that."
'DUP not no-deal party'
She said that she wants to see a sensible deal that works for Northern Ireland and "our neighbours down here in the Republic of Ireland".
"But one that works for the UK constitutional position as well. That's very important and one I hope the European Union will respect," she said.
Mrs Foster added that the DUP is often incorrectly pitted as a no-deal party.
"I think the sort of presentation that the DUP deal is a no-deal party is wrong and I think people get very alarmed when they hear that sort of rhetoric," she said.