His remarks come after DUP leader Arlene Foster expressed alarm at the contents of a letter from Mrs May which her party is interpreting as creating the potential for a post Brexit border in the Irish Sea.
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 hope to reach in the coming days.
In the leaked letter, the prime minister also told the DUP she "would not accept being kept in a backstop arrangement indefinitely", while it would be "totally unacceptable" for a time limit to the UK-wide backstop arrangement to then simply result in the Northern Ireland-only solution being adopted.
Sinn Féin MLA Máirtín Ó Muilleoir said the British government needed to honour its commitments to avoid a hard border rather than promises made to the DUP.
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. "For us it is a violation of the promise that was given that will be done, that we were cut off from the rest of the United Kingdom".
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.More news: Nedbank Gold Challenge - Four Southern Africans to watch out for
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Britain's culture minister Jeremy Wright arrives In Downing Street.
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.
"It can not be negotiated downwards. A successful outcome is not guaranteed but I think it is possible in the next couple of weeks", Mr Varadkar said.
Downing Street has played down suggestions that a Brexit deal is imminent, after the European council president, Donald Tusk, appeared to indicate a breakthrough could come within the next week.
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.
Brexit has come to the fore at today's meeting of the British Irish Council.
Ms Sturgeon also said that if a deal proposed by the UK Government can not command a majority in the House of Commons, it should not mean that departing the European Union with no deal is "inevitable".