The Irish Government said Mrs May and Mr Varadkar had discussed a "review mechanism" in which the backstop could be ended by mutual consent.
However, there have been reports the bloc could yet call an extraordinary gathering of national leaders towards the end of November following recent signs of progress.
"She said that while the United Kingdom should aim to secure a withdrawal agreement as soon as possible, this should not be done at any cost".
"This includes ensuring that if the backstop is ever needed it is not permanent, and there is a mechanism to ensure the United Kingdom could not be held in the arrangement indefinitely", he said.
The prime minister told cabinet that they would have another meeting before any agreement was settled, with No 10 insiders concerned a deal should be agreed by the end of this month if it is to be voted on before the United Kingdom leaves the EU.
Mr Varadkar told her that the European Union would never accept an arrangement that allowed Britain unilaterally to pull the plug on the "backstop". "Backstop means backstop. And a backstop can not have a time-limit".
Speaking in the Irish parliament on Tuesday, Mr Varadkar repeated his red lines.
Russian jet intercepts US Navy plane over Black Sea
A Russian Su-27 Flanker flew within five feet of an EP-3's wing tip over the Black Sea in January, Navy officials said. U.S. officials said Russia's military could exercise within worldwide airspace, but the pilot's behaviour was wrong.
However, the Irish prime minister added it may be to Ireland's "advantage" for a review clause to be included in a backstop agreement.
"There can be no expiry date and there can be no unilateral exit clause, and if it were to be either of those things, the backstop would not be worth the paper it was written on", he said.
Work is continuing on this, he said, adding: "Don't be under any illusions that there remains a significant amount of work to do".
The EU's chief negotiator Barnier himself said a breakthrough on the Irish border issue was not close.
Prime Minister Theresa May called a meeting Tuesday in what pundits say was a last ditch attempt at persuading colleagues to back a plan that could ultimately see all of the United Kingdom remaining inside the EU customs union, with all that would entail, in the event a Brexit-trade deal cannot eventually be reached.
The European Commission Vice President warned: "Should we need to act, we would only do so to the extent necessary to address financial stability risks arising from an exit without a deal, under strict conditionality and with limited duration".
"Can't understand why Irish Government seems so intent on this course".
Asked if Labour would vote against a customs union option unless it was permanent, Mr McDonnell told BBC2's Newsnight: 'Yeah, I think so, because... we'll see what she comes back with and we will be straight and honest with people, if it doesn't protect jobs and the economy we can't support it.
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