The Irish Prime Minister Leo Varadkar said the deal was "politically bullet-proof" and "cast iron".
The Irish government's chief whip, Joe McHugh, branded the Brexit Secretary's comments as "bizarre".
He told RTE: "We will as a government, a sovereign government in Ireland, be holding the United Kingdom to account, as will the European Union.
"My question to anybody within the British Government would be, why would there be an agreement, a set of principled agreements, in order to get to phase two, if they weren't going to be held up? That just sounds bizarre to me.
"This, as far as we're concerned, is a binding agreement, an agreement in principle."
The terms of the agreement specified "full alignment" with the EU on regulations on issues relating to "North-South co-operation" on the island of Ireland, which might include energy and agriculture. Responding to criticism of this agreement from Conservative Brexiteers who want to end all alignment with EU regulations, Mr Davis said: "This was a statement of intent more than anything else.
"Much more a statement of intent than it was a legally enforceable thing."
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