"Today we are launching negotiations on the orderly withdrawal of the United Kingdom from the EU", said Barnier, a former European commissioner and French foreign minister.
For many Brexit advocates, those conditions would be impossible to accept as last year's referendum campaign focused on getting back control over laws and immigration from the EU.
While the European Union negotiating team led by Barnier has been ready for months, British efforts on Brexit stalled even after it triggered the two-year process on March 29.
But May's failure to win a majority in last week's election has weakened her position badly and reopened the debate around the Brexit strategy just days before the country opens its divorce talks with Brussels on Monday.
"The UK has been crystal clear in our approach to the negotiations, the withdrawal process can not be concluded without the future relationship also being taken into account".
Asked if that meant no transitional arrangements, she replied: "Well, I'm extremely optimistic that we will find there is a lot we can agree on".
The talks will be in English and French, they said in a joint statement.
A beaming Brexit Secretary David Davis, a veteran campaigner against European Union membership, told a sombre Michel Barnier, the EU's chief negotiator, on Monday (Tuesday NZ Time) that his team aimed to maintain a "positive and constructive tone" during "challenging" talks ahead in the hope of reaching a deal that was in the interests of both sides.
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Trump returned to the White House on Sunday after spending Father s Day weekend at the Camp David presidential retreat. I really, truly believe that. "This issue will be addressed in due course and I suspect next week", Sekulow concluded.
Leaving the European Union was once far-fetched: only 15 years ago, British leaders were arguing about when to join the euro, and talk of an EU exit was the reserve of a motley crew of skeptics on the fringes of both major parties. While denying they want to punish their neighbour, European Union officials have warned Britain off trying to "cherry pick" the benefits of membership and said it will be left worse off outside the bloc than inside. "But the 27 of us will formulate our interests very clearly and hopefully, together", Merkel said.
Leaving the EU - the biggest blow since World War Two to European efforts at forging unity - is now the official consensus of both the Conservatives and the opposition Labour Party.
With discontent in Europhile Scotland and troubled Northern Ireland, which faces a new European Union border across the divided island, Brexit poses new threats to the integrity of the United Kingdom.
"The best way we can spend this week is to rebuild trust", rather than tackle the big hard issues right at the start, a European source said.
He said: "We have to commit ourselves now mutually to guarantee rights to citizens on either side of the Channel so they can continue their lives as in the past".
Still, British Foreign Secretary Boris Johnson remained upbeat Monday and thinks that the Brexit negotiations will yield "a happy resolution that can be done with profit and honour for both sides". "In the first step we will deal with the most pressing issues, in the second step will scope our future partnership", added Barnier.
Mr Barnier did not put a figure on the settlement likely to be required from the United Kingdom, estimated by some in Brussels at as much as 100 billion euro (£88bn).
"No deal would be very, very bad outcome for Britain", Hammond said Sunday.
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