The Taoiseach has welcomed a vote in the House of Commons, which enables the British government to ask the European Union for a delay to Brexit.
MPs want to delay the UK leaving the EU until at least the end of June. The motion by the British government was approved by 412 votes to 202.
In a statement, Leo Varadkar said that the result of the vote reduces the likelihood of a no-deal Brexit.
However, he said that London needs to give details on what purpose an extension would serve, and how long it would last for.
He said: "There seem to be two emerging options: ratification of the withdrawal agreement followed by a short extension into the summer, or a much longer extension that would give the UK time and space to decide what they want to do, including considering options that had been taken off the table like participation in the customs union and single market.
"I think we need to be open to any request they make, listen attentively and be generous in our response."
Earlier, Tánaiste and Minister for Foreign Affairs Simon Coveney has said a Brexit extension of 21 months is a possibility.
He said a long extension would give the UK a "long reflection period" about the kind of Brexit it wants and may facilitate a fundamental rethink, or it may not.
Speaking on RTÉ's Today with Sean O'Rourke, Mr Coveney said a "crash-out" could happen by accident even if most people do not want it, but he thinks the UK will get an extension as long as there is a plan to go along with that.
He said British Prime Minister Theresa May has a choice of "one or the other" - an extension or her deal.
He said Mrs May is providing a stark option to accept a deal by next Wednesday and face a short extension of time to leave the EU, or to not agree a withdrawal agreement and face a much longer wait for Brexit.
However, he said Ireland will continue to prepare for a no-deal Brexit and the Government hopes that over the next week Brexit will take a positive turn that will provide more certainty.
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Last night Mrs May said that the move could involve a short delay to implement a deal agreed in the next few days, or a longer delay if no agreement is reached.
Mrs May's government has also set out plans for a third parliamentary vote on her Brexit deal with the EU to be held by 20 March.
MPs voted in favour of an amended motion last night, which rejected the UK crashing out of the European Union without a deal at any time under any circumstances.
In a surprise move, the House of Commons voted 312 to 308 - a majority of four - in favour of the amendment.
Events in the House of Commons last night mark a turning point for Brexit, he said.
It is "very reassuring to show that they don't want to crash out of EU without a deal".
It comes as European Council President Donald Tusk said he would ask EU heads of state and government to be open to granting Britain a long extension of Brexit talks if London needs time to rethink its strategy of leaving the EU.
"I will appeal to the EU27 to be open to a long extension if the UK finds it necessary to rethink its Brexit strategy and build consensus around it," Mr Tusk said on Twitter.
EU leaders meet to discuss Brexit on 21-22 March.