Theresa May is to tell the European Union to "evolve" its stance on Brexit, warning that previous positions are "unworkable".
The Prime Minister will use a speech in Belfast on Friday to reiterate her refusal to contemplate any backstop deal that treats Northern Ireland differently from the rest of the UK.
She is due to say that any such deal would go against the Good Friday Agreement, which brought peace to Northern Ireland 20 years ago after decades of conflict.
Mrs May will say that following the publication of the Government's white paper agreed at Chequers, it is "now for the EU to respond".
She will add: "Not simply to fall back on to previous positions which have already been proven unworkable. But to evolve their position in kind.
"And, on that basis, I look forward to resuming constructive discussions."
The EU's other 27 states will have a chance to examine and respond to the white paper when its General Council of ministers meets in Brussels on Friday morning.
They will also receive an update on negotiations from the European Commission's chief negotiator, Michel Barnier.
The Irish border issue is one of the most disputed parts of the Brexit negotiations.
In the event of a hard no-deal Brexit, the EU wants a backstop that would effectively create a border down the Irish Sea between the island of Ireland and Great Britain, something Mrs May has repeatedly opposed.
The UK Government insists that any backstop position should include the UK as a whole.