"David Davis and I, as chief European Union negotiator, will discuss the issues together, tackle difficulties, and lift obstacles", he added.
British Prime Minister Theresa May's programme for government is revealed at the formal opening of parliament on Wednesday after an election that weakened her authority and tragedies that have shaken the nation.
Sir Keir Starmer, the shadow Brexit secretary, refused on Sunday to say whether Labour would support the Great Repeal Bill, saying he would wait to study the legislation.
"I look forward to working closely with you during this negotiation", EU negotiator Barnier said, as quoted by the press service of the European Commission, the EU's executive.
"In the first step, the negotiation rounds will be broken down into three groups - citizen rights, the single financial settlement, and other separation issues", Barnier said.
The most senior officials on either side will lead work on efforts to resolve the problem of the border between Northern Ireland and the Republic of Ireland, a situation Mr Barnier acknowledged was "politically sensitive" at a time when the Tory government was seeking the support of the Democratic Unionist Party to prop up Mrs May's minority government.
So instead of London starting out with the contours of a deal that could preserve its access the huge European Union market, it must face months of detailed talks over what kind of rights European Union citizens in the United Kingdom will have - and what rights Britons on the continent will enjoy.
"There may well be the need for certain transitional periods, some of them which will involve phasing out, others potentially phasing in", Barnier told reporters in Luxembourg after a meeting of European Union affairs ministers.
Kia tops new car quality survey for second straight year
Fiat Chrysler Automobiles NV's FCAU.N Ram and US automaker Ford Motor Co's F.N namesake brand shared the fourth position. Kia came out on top with only 72 reported issues per 100 owners, which dropped from 83 reported issues in 2016.
Britain is "very conscious of how they will use that time sequence to pressure us, and we'll avoid that at every turn", Davis told ITV on May 14.
"It's not when it starts it's how it finishes that matters", he said.
The Union wanted a "fair deal", he said, renewing a vow not to punish Britain or take "revenge" for a withdrawal that has rocked the bloc and poses huge challenges for negotiators.
"They should be agreed alongside each other, this is completely consistent with the Council's guidelines which state nothing is agreed until everything is agreed".
Frenchman Barnier struck a firm tone as he said the timetable for Britain's divorce after four troubled decades of membership made sense.
"The question then will be: is it better to have freedom to strike new deals across the world or are we better off staying with deals that are struck by the EU?"
"So, we each have to assume our responsibility and the consequences of our decisions".
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