Both EU negotiator Michel Barnier and his United Kingdom counterpart David Davis said they were heartened by the first day of talks on Monday and insisted the tight deadlines were tough but achievable.
In Berlin, German Chancellor Angela Merkel emphasised the unity of the remaining 27 European Union countries, who have been alarmed in recent weeks by May's threats to walk out of the talks.
Barnier however said that "a fair deal is possible and is far better than no deal - that is what I said to David today".
Barnier said there was agreement that the negotiators would first look at citizen's rights, the outstanding bill Britain must pay for previous European Union commitments and the Irish border issue.
If May wants to remain in power, she must change her approach to the Brexit negotiations. For the officials sitting down on Monday, at least on the European Union side, a major worry is Britain crashing out into a limbo, with no deal.
But Mr Soros predicted it would take until as long as 2022 for the Government to secure a favourable trade deal.
"It's not when it starts it's how it finishes that matters", he said.
The election had been called by the Conservative Party with the intention of consolidating its hold over United Kingdom politics.
Davis said Prime Minister May will also set out at an EU summit on Thursday her proposals for the rights of the three million EU nationals living in Britain, and one million Britons in the EU, with the British government to publish a detailed offer next Monday.
"It's not about punishment, it is not about revenge".
Family declines autopsy for United States student released by North Korea
Otto Warmbier, 22, died at a hospital in Cincinnati, Ohio on Monday, a week after being released from North Korea in a coma. Wambier's parents did not cite a specific cause of death but blamed "awful, torturous mistreatment" by North Korea.
"And the consequences are substantial". In his first major comments in six weeks, he also said he wants to see how the economy responds to the "reality of Brexit negotiations".
"The pessimist see difficulty in every opportunity, the optimist sees opportunity in every difficulty".
The announcement was made alongside the start of discussions with the European Union on Brexit on June 19.
"We are citizens first".
After Davis and Barnier met over lunch in the Commission's top floor dining rooms, their teams broke up into "working groups" that will be charged with handling specific areas of talks that the European Union expects to take place for a week every month.
"In the first phase, the negotiation rounds will be broken down into three groups: citizens' rights, the single financial settlement, and other separation issues", Barnier said.
The Brexit talks were finally launched at the European Commission's headquarters in Brussels almost one year after Britain's June 23, 2016 referendum to leave the bloc.
The terms of reference state "for both parties the default is transparency" and that it is for the side providing any information to state whether it should remain secret.
Mr Barnier spoke at a press conference after the first day to confirm that settling priority issues would build "trust on which to negotiate a new relationship". "A soft or flexible Brexit we read as no Brexit and that we will not countenance". "It was a clear rebuff to May's stated ambition of wrapping up a new free trade agreement quickly".
Davis described the timetable as a "promising start" to the Brexit process."As you heard Michel said, we had a brief exchange earlier about the distinction between being optimistic and being determined".
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