DUP leader Arlene Foster has criticised a Northern Ireland-only backstop as "anti-democratic and unconstitutional".
Mrs Foster also said that Boris Johnson has previously ruled out the option of having the backstop applying only to Northern Ireland.
Following a meeting between Boris Johnson and Taoiseach Leo Varadkar in Dublin, Mrs Foster said she was "encouraged" by the British prime minister's commitment to getting "a sensible deal".
"I hope the discussions in Dublin lay the foundation for a way forward," she added.
"We want the referendum result implemented. To do otherwise would be to damage democracy, but we have never been champions of exiting the European Union without a deal.
"To secure a sensible deal which respects the economic and constitutional integrity of the United Kingdom will require pragmatic discussions on all sides.
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"The prime minister has already ruled out a Northern Ireland-only backstop because it would be anti-democratic, unconstitutional and would mean our core industries would be subject to EU rules without any means of changing them.
"We will continue to work with the government and will also use any discussions with the taoiseach to encourage efforts towards a sensible deal."
A Northern Ireland-only arrangement would mean an all-island regulatory alignment that would see Northern Ireland moving away from the rest of the UK.
It was previously offered by the EU during the Brexit negotiations, but the DUP rejected it.
