"Before we break for the summer in the Commons we'll be taking the other two bills that need to be addressed that are relevant in relation this issue", Mrs May said.
At the heart of the problem is ensuring there is no hard border between the British province of Northern Ireland and the Irish Republic, which will remain in the EU.
"The PM has been clear that we will preserve the integrity of the U.K.'s internal market and there will not be a customs border down the Irish Sea - any backstop option will satisfy this", he said.
"The UK calls this arrangement "temporary", said Mr Barnier.
Foreign Secretary Boris Johnson said at a private dinner that there's a risk of a Brexit "meltdown", but that no one should panic over it.
The EU has rejected all Customs Union and Irish border solutions put forward by the United Kingdom so far, including the "Max Fac" option allowing the United Kingdom to break free of EU rules and keep the Irish border open.
This will see the UK retain parts of the EU's customs union in the event of a wider UK-EU agreement finding no solution to the issue; but Brexiteers had become concerned as to whether the proposal would truly be "time-limited", as promised.
He questioned whether a temporary backstop could "secure the absence of a hard border in all circumstances" and said it might mean businesses and public authorities having to cope with several changes.
May's ministers are split on what kind of customs deal Britain should seek from the European Union ahead of a summit of the bloc's leaders which will try to make progress on the stalemated Brexit negotiations this month.
But Charlie Elphicke, who represents Dover and Deal, said there was "scepticism" over HMRC's figures, telling Mr Thompson that most estimates put Brexit customs costs at 1% of trade value rather than 5%.
The pro-EU Best For Britain claimed the UK's backstop plan was "dead on arrival" in Brussels.
Britain now expects the future arrangement to be in place by the end of December 2021 at the latest, a year after the end of the post-Brexit transition period.
When asked how respondents would like to see Northern Ireland governed, 42.1% said they would choose a devolved Northern Ireland Executive at Stormont.
His comments come ahead of a crunch European Union summit in Brussels at the end of the month, where the European Union hopes to resolve matters such as the Irish border issue.
And Labour MP Ian Murray, a supporter of the People's Vote campaign for a second referendum, said: "Theresa May's flimsy Brexit proposal has lasted less than 24 hours".
China issues statement on Sino-US trade talks
China has promised to "significantly increase" purchases of farm goods, energy and other products and services. Mnuchin had said on Saturday the United States wanted China to agree to structural change to its economy.
Portugal vs. Algeria - Football Match Report
Portugal's Cristiano Ronaldo set up one goal and had another disallowed against Algeria on Friday. Portugal will begin its World Cup campaign against Iberian rival Spain on June 15 in Sochi.
Russian Federation not trying to split EU: Putin
Moscow retaliated in kind but Putin has repeatedly said the sanctions were ineffective and counter-productive. One read, "Our lives are getting worse and worse". "It's in the Kremlin where everything is wonderful".
James has carried Cavaliers as far as he can
Iguodala, the 2015 finals MVP, scored eight points and made one steal in 22 minutes, but his impact went beyond those numbers. James historic night was put in jeopardy in the second quarter when he turned his right ankle on a drive to the basket.