The DUP are ignoring the evidence from our business community, our farming industry and from citizens the length and breadth of Ireland, who support a bespoke arrangement that meets our particular needs and reflects our particular realities.
But DUP leaders said on Friday that May's wording meant the fix would still be included in the withdrawal agreement that London and Brussels have been arguing about for many months.
DUP leader Arlene Foster said the Prime Minister appeared "wedded to the idea of a border down the Irish Sea" despite Downing Street's repeated assurances to the contrary.
"From her letter, it appears the prime minister is wedded to the idea of a border down the Irish Sea with Northern Ireland in the European Union single market regulatory regime", Foster said.
Some British media said May's government leaked the letter to prepare the ground for what The Guardian called a final "showdown" with the DUP over the checks.
The DUP has accused the PM of breaking promises over plans to avoid a hard border in Northern Ireland post-Brexit.
The DUP has seized on a particular paragraph- which has been seen by the Times - in which May said she could not accept circumstances or conditions that could break up the United Kingdom customs territory to come in to force.
Malibu Under Evacuation Orders as Massive Fire Rages
The Hill Fire is the other fire burning near the site of this week's mass shooting in Thousand Oaks . Around 10,000 acres of land was torched in the blaze by Thursday night, fire officials said .
"From what we can see in the letter which has been sent to Arlene and Nigel (Dodds), it is quite clear some of the promises made do not conform to some of the content of the letter".
Britain's culture minister Jeremy Wright arrives In Downing Street.
Any version of the backstop would apply unless and until a wider UK-EU deal on the future relationship solved the issue of how to avoid a hard border with Ireland.
She said: "I will make no bones about the fact that the Brexit experience has exposed real weaknesses within the devolution settlement that will require them to be worked through and resolved along the way".
Almost a year ago, its refusal to sign off on a deal on the border caused the temporary collapse of Brexit talks at a crucial stage.
Scottish First Minister Nicola Sturgeon was among the leaders at the Isle of Man summit and urged Tory leaders to consider keeping the whole of the United Kingdom in the single market, warning that Brexit has highlighted "real weaknesses" in the UK's devolution settlement.
The First Minister was speaking following a meeting of the British-Irish Council on the Isle of Man, which was also attended by Welsh First Minister Carwyn Jones and Ireland's Leo Varadkar.
The Taoiseach says a deal on Brexit is still possible within weeks.