With the Brexit negotiations stalling and British Prime Minister Theresa May failing to offer any further solutions to avoid a hard border between Northern Ireland and the republic, Varadkar's comments came before his meeting with the UK leader at an EU summit in the Bulgarian capital Sofia.
Varadkar said that June's European council summit would be a key moment for the talks despite attempts by the Brexit secretary David Davis and others in the UK government to play down suggestions of a "deadline", the Guardian reported.
The UK government had vowed to find an arrangement that will avoid the need for border checks between the Republic of Ireland and Northern Ireland and to table a "backstop" solution involving regulatory alignment with the EU.
Varadkar said: "We need to have that backstop because that gives us the assurance that there will be no hard border on our island. So we stand by our position that there can be no withdrawal agreement without that backstop.
"If the UK wants to put forward alternatives we're willing to examine that. But we need to see it written down in black and white and know that its workable and legally operable. And we've yet to see anything that remotely approaches that."
Earlier this week, the British government promised to produce a 100-page white paper on the future trading relationship.
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