On this point, the agreement — which still has to be approved by European Union leaders when they meet in Brussels later this week — was deliberately ambiguous and open to different interpretations. But it seemed to say that the United Kingdom would stay in the bloc’s single market and customs union if that was what was needed to avoid a hard border.
But that statement was a step too far for Britain’s hard-line Brexiteers, so David Davis, the Brexit secretary, apparently walked it back on Sunday, infuriating the Irish government and raising familiar questions in European capitals about the coherence of the British government position.
Mr. Davis described the careful pledges about the border not as the government’s definite position but as a “statement of intent” and not something “legally enforceable.”
In one respect he was correct, as the accord is a political agreement that will become legally binding only once it is part of an overall international agreement. Yet by suggesting that this might never happen, Mr. Davis strayed into dangerous territory of appearing to undermine his government’s commitment to it.
He also told the BBC that Britain’s financial offer, or “divorce bill,” to the European Union — which he estimated at $47 billion to $52 billion — was contingent on a “trade outcome,” adding that in the absence of such a deal, Britain “won’t be paying the money.”
Meanwhile, the environment secretary, Michael Gove, argued that what had been agreed on Friday could ultimately be changed to allow Britain to diverge more from the European Union rules, if voters elected a different government in the next elections.
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On Monday, Mrs. May herself confirmed Mr. Davis’s figure for Britain’s financial payments, adding that the pledge to pay the cash was made “in the context” of an overall exit agreement. However, that was tempered by Mrs. May’s statement that Britain was a country “that honors our commitments.”
The episode illustrates the complexity of her predicament as she seeks to juggle competing — sometimes irreconcilable — interests, and as members of her Conservative Party put their own spin on events — in the case of pro-Brexit lawmakers minimizing the significance of British concessions.
On Monday, Mr. Davis seemed to walk back the statements he had made on Sunday, telling LBC Radio that the deal was “much more than legally enforceable,” a comment that was welcomed by Ireland’s prime minister, Leo Varadkar.
In Parliament, most Conservative lawmakers were supportive of their prime minister, though several asked pointed questions. Jeremy Corbyn, leader of the opposition Labour Party, said Mrs. May had “scraped through” the first round of negotiations, noting that some of her cabinet ministers had managed to contradict one another — or even themselves.
While there is no evidence that British voters have clearly changed their views on Brexit, surveys suggest that even those who say they voted to leave have noticed that the government is struggling to manage a negotiation that some leading Brexit supporters once presented as simple.
Their faith in its negotiating ability may not have been bolstered by another comment made on Monday by Mr. Davis, when he described the skills needed to perform his job.
“I don’t have to be very clever,” he said. “I don’t have to know that much. I just do have to be calm.”