The Taoiseach and the new British Prime Minister appear to be on a collision course over Brexit.
In his first address to Parliament in the top job, Boris Johnson called for the complete removal of the backstop from the Withdrawal Agreement.
Mr Johnson said that will be a key objective for him in negotiations with the European Union.
He said today: "No country that values its independence, and, indeed, its self-respect, could agree to a treaty which signed away our economic independence and self-government as this backstop does.
"A time limit is not enough if an agreement is to be reached it must be clearly understood that the way to the deal goes by way of the abolition of the backstop."
However, Leo Varadkar has said the backstop is essential to any agreement and can not be dropped.
He warned Mr Johnson that Britain will not secure a free trade deal with the EU without the backstop
"The position of the European Union and the position of Ireland has not changed," the Taoiseach said. "The backstop is an integral part of the Withdrawl Agreement."
"Without the backstop, there is no Withdrawl Agreement, there's no transition phase, there's no implementation phase and there will be no free trade agreement until all those matters are resolved.
"So I hope that the new UK Prime Minister hasn't chosen no-deal, but that will be up to them."
Last night, Mr Varadkar said the new British PM's comments on the backstop are “not in the real world”.
On taking office yesterday, Mr Johnson at Downing Street declared: “Never mind the backstop, the buck stops here.”
However, his comments drew stinging criticism from Mr Varadkar who said Mr Johnson's comments were “clear cut but certainly not detailed.”
The backstop is an insurance policy intended to prevent the imposition of a hard border on the island of Ireland if no overarching trade deal is agreed between Britain and the EU.
The backstop would entail Northern Ireland remaining aligned to the EU’s regulations after Brexit.
The DUP and Tory Brexiteers blocked ratification of the withdrawal agreement by Parliament earlier this year over concerns the measure could threaten the integrity of the UK.
Democratic Unionists want a time limit to be put on the backstop, a provision rejected by Ireland as rendering it meaningless.
- additional reporting by Press Association