"We stressed again the need to respect the constitutional position of Northern Ireland and the economic integrity of the United Kingdom single market", she said after meeting Michel Barnier, the European Union's chief Brexit negotiator, in Brussels.
While May dismissed the European Union text as unacceptable, Chancellor of the Exchequer Philip Hammond told lawmakers on Monday there were no plans to present an alternative draft treaty before a summit later this month.
Arlene Foster on Tuesday warned the European Union and Theresa May that her Democratic Unionist Party would torpedo any Brexit deal that created a new border in the Irish sea between Northern Ireland and Britain.
The draft withdrawal treaty was instead said to amount to an unjustified attempt by Brussels to revise the terms of the Good Friday agreement, which has kept the peace since 1998.
"That is his interpretation, we don't think it's a fair interpretation of the joint report from December and therefore work needs to be done on this now".
The border between the UK and Ireland can not be transformed in the image of the border between the USA and Canada, Ireland's Prime Minister Leo Varadkar said on Monday, after the UK Prime Minister Theresa May floated the idea before the UK parliament. At the same time, May gave an assurance that no barriers between Northern Ireland and the rest of the United Kingdom will come into play. "What continues to be critical for Ireland is that the guarantees that we need regarding how a hard border be avoided, that those guarantees be maintained". "It would be an economic catastrophe if we allowed a border between ourselves and the rest of the U.K".
Describing her talk with Mr Barnier as "good and very open", she insisted the text has "omissions in it" and said it "also overreaches in other areas".
And Nigel Dodds, Mrs Foster's deputy and the DUP's Westminster leader, also blasted Mr Barnier's proposals.
"There are three options in relation to future relations, this [legal text] has only reflected the third of those options, it doesn't reflect the first and second". May had repeatedly stated there would be no hard border on the Irish island after Brexit.
Those proposals should not be flippantly dismissed, Foster said.
He has said that it is incumbent on anyone who is unhappy with the draft text to bring forward legally enforceable alternatives.
"What emerges clearly from this research is the high degree of integration of the economies north and south". She said that the infrastructure on that border largely related to checking the movement of people rather than goods, which moved freely.