At a meeting on Tuesday, the prime minister reassured Brexit-backing members of her party that she will deliver the kind of Brexit they want and will take Britain out of the customs union., according to two people familiar with the conversation.
Davis also said that the Commons motion on the final Brexit deal, expected this autumn, could be amended by MPs.
The UK has previously declared that once it withdraws from the European Union, it would no longer fall under European Court of Justice jurisdiction, but now Barnier has revealed that the EU will insist on ongoing judicial oversight for the court remain part of any prospective Brexit deal.
Earlier, Downing Street issued a sharp correction after home secretary Amber Rudd appeared to cast doubt on the government's determination to leave the customs union.
She later again said that the government's position was to leave the customs union, which sets external tariffs for goods imported into the bloc, so that Britain can independently negotiate trade deals with other countries.
The contract, which was awarded in January, ended last month, on the same day the government secured European Council backing for a transition deal that unlocked the current round of Brexit talks on Ireland and the future relationship.
Nigel Dodds, DUP head in parliament, said his party will vote against Mrs May's minority Conservative government if any of the "red lines" on Brexit are crossed.More news: Comcast makes £22bn bid for Sky plc, 16% premium on Fox's offer
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Her comments provoked anger among Leave-supporting Tories who accused her of trying to undermine the Prime Minister.
As this archly annotated Credit Suisse deck points out, May only has one real option left: Staying inside the EU's customs union.
A "customs partnership" that would involve the United Kingdom collecting the EU's tariffs on goods coming from other countries on the EU's behalf is under consideration, along with proposals for minimised checks using technology and a trusted trader scheme.
Nigel Dodds, who heads the DUP in the London parliament, said his party will vote against Mrs May's minority Conservative government if any of these so-called "red lines" on Brexit are crossed.
Despite previous negotiation deadlocks, the European Union has said it is open to discussion.
"It seems rather perverse that at a time when we want to increase free trade, we're going to put up a whole load of barriers to stop access in that best free trade area that is existing in the world", said Conservative MP Anna Soubry.
Vocal pro-Brexit campaigners have also held her to her position on the customs union, leaping to protest at any hint she could seek a compromise on ties to prevent a return of a hard border that might reignite sectarian violence. "The answer is categorically yes".