Mrs Foster said: "The Prime Minister's letter raises alarm bells for those who value the integrity of our precious union and for those who want a proper Brexit for the whole of the UK".
The party accused the prime minister of breaking a promise that that she would never sign up to a deal that treated Northern Ireland differently from the rest of the UK.
Varadkar said that while the DUP was important, there were other voices in Northern Ireland. They said May had earlier promised them it never would, and they threatened to vote against the agreement. "There were people saying to us, if we can't sell our cheddar cheese to the English, the French don't want it, the Germans don't want it, how do you actually begin to deal with all of that?", Mr Fealty said.
The spokesman also noted that UK Prime Minister's Theresa May stance in negotiations is a betrayal and she has breached the promise.
Downing Street says the letter sets out the prime minister's commitment "to never accepting any circumstances in which the United Kingdom is divided into two customs territories".
Tensions between Mrs May and her DUP allies have been exposed amid concerns about measures aimed at avoiding a hard border on the island of Ireland.
This would apply if a future EU-UK trade relationship failed to avert a hardening of the frontier between Northern Ireland and the Republic of Ireland.
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Pittsburgh Steelers wide receiver Antonio Brown has been cited for driving in excess of 100 miles per hour on McKnight Road. Per the report , Brown was initially pursued because the officer was looking for a fleeing suspect from a bank robbery.
"The PM knows the consequences, she now needs to reconsider", DUP lawmaker Sammy Wilson said.
"It must be built on to ensure our rights are protected and translated into legally operable and binding text as part of any withdrawal agreement".
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 warning underscores the travails that May faces in getting any Brexit divorce deal, which London and Brussels say is 95 percent done, approved by both her fractious party and by the Northern Irish lawmakers who keep her in power.
But David Lidington, Mrs May's de facto deputy prime minister, said he hoped that once a deal was on the table MPs would rally behind it.
A potential sticking point could be demands for European Union fishing fleets to be given continued access to British coastal waters as the price for agreeing to Mrs May's UK-wide backstop, the Daily Telegraph reported.
"Secondly, it would be a legal agreement which the government of the United Kingdom could not walk away from - that could only be broken if the government in the United Kingdom and the European Union agreed to it being changed".