The Taoiseach says it's not for him to call for a second Brexit vote of but that it "wouldn't be anti-democratic" for the UK to hold another poll on leaving the EU.
Mr Varadkar was responding to speculation that the British government could arrange a second vote due to the lack of clarity over what Britain leaving the EU actually means.
The idea was recently mooted by an unlikely protagonist Nigel Farage who claimed doing so would put to bed any claims by those of the Remain side that people had changed their minds.
However, others say the result of a new vote would overturn Brexit.
Mr Varadkar was taking part in a special leaders' debate on the future of Europe.
He was the first of all EU heads of government to address the Parliament in Strasbourg and was also forced to deny an accusation by Mr Farage that he was part of a conspiracy alongside former British PM Tony Blair to stop Brexit.
The former Ukip leader said he "fears" the Taoiseach is "working together with Nick Clegg and Tony Blair" to make sure the UK gets the "worst possible deal" on Brexit thereby forcing the British into a U-turn.
The Taoiseach categorically denied he was "involved in any plot".
"I've never met Tony Blair and I'm certainly not involved in any plot for a second referendum", he said.
When asked if he would welcome a second vote on Brexit, Mr Vardakar responded: "I don't think it would be constructive or helpful for the leader of another country to be advising that other country on whether they should or should not have a second vote."
But he said that Ireland has held second votes on issues in the past but "nobody told us we had to".
"They were decisions we came to ourselves," Mr Varadkar said.
"And, of course, we had second votes on matters other than European matters.
"The Irish people in the 1980s chose not to remove our constitutional ban of divorce but we thought about it again and made a different decision.
"And we decided in 1983 to introduce a constitutional ban on abortion and we're going to be asking people to think about that again this year.
"So I don't think it's anti-democratic to change your mind or have a second vote", he added.
The Taoiseach also spoke about how Brexit personally affects him and that he still "cares" about Britain.
He said Ireland was a country that is close to Britain in so many ways "even though we sometimes don't like to admit that."
He told the Parliament that his parents "met and fell in love" in the UK and had their first child, his sister there. He said his sister and her children live there now and his niece and nephew point to the Union Jack as "their flag".
Mr Varadkar also said it's a "real shame" that children in their class will lose the automatic right to live and work in Europe because of Brexit.