The Taoiseach has said he is satisfied with the draft conclusions agreed at the European Council summit last night, which says the Withdrawal Agreement for Britain to leave the EU is not open for renegotiation.
Last night, EU leaders rejected Mrs May's call for legally binding assurances on the Irish backstop and ruled out any changes to the Withdrawal Agreement.
Speaking to the media in Brussels, Mr Varadkar said it was agreed that the EU should begin talks on the future relationship with the EU once Westminster approves Theresa May's Withdrawal Agreement.
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Mr Varadkar said the council underlined its support for the backstop as an insurance policy to prevent a hard border.
He said it was an all-weather guarantee that there will never be a hard border on the island of Ireland.
The Taoiseach said that was important so that all sides can enter the talks on future relations without fear of a potential hard border being used as leverage.
Speaking this afternoon, Minister for European Affairs Helen McEntee said it was clear from European colleagues that the EU27 is continuing to support the backstop and the Withdrawal Agreement.
Earlier today, Mr Varadkar said: "We don't believe it's up for renegotiation, we're very keen to begin, as soon as it's ratified, talks on the future relationship, because we want to have a close relationship with the United Kingdom.
"As Europe we reaffirmed our commitment to the need for a backstop, and not just because it protects Ireland and ensures no hard border between Northern Ireland and Ireland, thus protecting the peace process and the Good Friday Agreement, but also because it's a European issue too, and an open border between Northern Ireland and Ireland can't become a back door into the single market."
Mr Varadkar said that was why other EU countries supported the backstop.
It was "very much a European issue," he said.
"We can ensure that no side uses the threat of a border in Ireland as part of leverage in the future relationship talks."
The Taoiseach said he was always willing "to offer clarifications, explanations, and we can discuss what form that takes, but what we won't be doing as a European Union is renegotiating the Withdrawal Agreement".
Mr Varadkar also said he thought a no-deal scenario was "unlikely".
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Mr Varadkar said that information on preparation for a no-deal Brexit is to be released by both the European Union and by Ireland next week.
He said he believes EU preparations will be made public on 19 December, while he understands Irish preparations will be released the following day, or on Friday 21 December.
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Mr Varadkar also said that there is no proposal for a special summit of EU leaders next month.
He said a lot of leaders were called to such a summit at the end of November and he did not believe they would be willing to come again at short notice.
"The next meeting is scheduled for the end of March," he said, adding there are no plans for any other meeting unless it is deemed necessary by Donald Tusk.
Mr Varadkar also said he does not believe a no-deal Brexit is inevitable, pointing out that Britain has the option of revoking or extending Article 50 if a deal cannot be gotten over the line.
He added that he does not believe an emergency Budget will be required in the event of a no-deal Brexit.
The Fine Gael leader said October's Budget provides for a surplus next year and a rainy day fund.
He also highlighted ESRI analysis that says even in the event of a no-deal Brexit, Ireland would experience economic growth of 3%.
"We're confident we won't have to have a new Budget in any circumstances," he said.
