Arlene Foster last night accused the Theresa May of trying to force people into backing her Brexit deal.
The DUP leader described her Tory counterpart's approach to Brexit as "weak" and damaging to the UK.
She made the comments ahead of her meeting with the EU's chief Brexit negotiator Michel Barnier.
She will be joined by Northern Ireland MEP Diane Dodds as well as Conservative MPs Iain Duncan Smith and Owen Paterson at Thursday's meeting.
"We want to see a sensible deal which works for every part of the United Kingdom and respects the referendum result," she said.
"However, we cannot settle for a deal which would undermine the economic and constitutional integrity of the United Kingdom."
Mrs Foster said the EU spoke a lot about protecting the peace process and the Good Friday Agreement but had ignored the views of unionists, who she said were opposed to a so-called border in the Irish Sea.
"Despite the prime minister being warned about the opposition to her withdrawal agreement, she has limped along and tried to force people into a cul-de-sac where they have no option but to support her deal," she said.
"That is a weak approach and demeans the strength of this great nation."
She said it was "outrageous" that almost three years after people voted to leave the European Union, the UK could potentially face another European election.
