The Irish border remains a key talking point during Brexit negotiations. Mr Varadkar also rejected proposals now being examined which would mean anyone crossing the border would have to pre-register in order to avoid checks.
Speaking from the United States, where he is conducting a series of St Patrick's Day engagements, Varadkar said: "No, it is not a solution that we envisage".
Varadkar urged senior cabinet figures such as Boris Johnson, who recently said the checks were an Irish/EU not a British problem, to visit the border.
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In December, a deal between the EU and the UK agreed that UK would maintain regulatory alignment with the EU's customs union if the UK could not come up with a solution for Northern Ireland that avoided a hard border.
Mr Varadkar said when he visited the US-Canada border he saw "a hard border...with customs posts, people in uniforms with arms and dogs".
"You can read as many briefing documents as you like, sometimes you need to see things with your own eyes".
"I think for that reason, they would be very welcome to visit the border and see it for themselves".
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He said that now differences in excise duties between Northern Ireland and Ireland are "policed by an intelligence-led approach with collaboration between police forces and customs authorities on both sides of the Border". Last week, Queen's University researchers concluded that technology could not make the border frictionless.
"Theresa May's order that Britain should leave the digital single market may mean that she has to pay more on a trip to the south of France but it will have a significant impact on people living in border communities or those who cross the border for work here. It can not make a hard border frictionless", said Katy Hayward, a political sociologist at Queen's University.
Due to the sluggish process of exit negotiations, German companies increasingly expect a "hard" Brexit in which Britain leaves the single market and loses most of its now privileged access to the European Union internal market.
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