DUP Brexit spokesman Sammy Wilson told Sky News that Ms.
In a tweet, Foster seized on May's insistence that she couldn't accept a deal that could see the break up of the United Kingdom customs territory.
Mr Varadkar's comments came after a leaked letter from Theresa May to the Democratic Unionist Party suggested a border down the Irish Sea could be included in the withdrawal agreement.
But the DUP has interpreted the wording of her letter to mean that the EU's proposal - known as the "backstop to the backstop" - will be contained in the Brexit divorce deal despite Mrs May's insistence it will never come into effect.
The Dup claim that according to the letter of the Prime Minister may, she is preparing to break the promise before the party, worrying that it would vote against the deal on Brexit in Parliament.
May, who marks the centenary of the end of World War One at ceremonies in Belgium and France on Friday, has repeatedly said she will not accept any deal that breaks up the United Kingdom. "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.
"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".
May depends on the 10 DUP MP votes for a majority in Westminster and will likely need them for any vote on a deal she strikes with Brussels.
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.
Less than five months before Britain is due to leave the European Union on March 29, negotiators are still haggling over a backup plan for the land border between British-ruled Northern Ireland and European Union member Ireland should they fail to clinch a deal.
The scope of any alignment with Brussels' rules would be limited to what is "strictly necessary" to avoid a hard border. It can not be watered down or bargained off.
TAOISEACH Leo Varadkar has claimed that a deal between Britain and the European Union on Brexit could be possible within a fortnight.
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.
Mr Varadkar said talks are at a "sensitive point" and a "successful outcome is not guaranteed but I think it is possible in the next couple of weeks".