This is despite proposed motions at a recent Young Fine Gael Summer School meeting calling for Mr Varadkar to step down if the party lost seats in the local or general elections.
One branch of the youth wing suggested debating motions "calling for the leader to resign after the next local election if more than 10% of seats won in 2019 are lost".
Another mooted Young Fine Gael should "call for the party leader to resign after the election if Fine Gael does not win 10 additional seats.
A spokesman for the Taoiseach said these motions were not debated.
Mr Varadkar added: "While a party's standing in a national election or a national opinion poll can affect the results of local elections, it doesn't necessarily follow through.
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