Two-thirds of those surveyed in Belgium, Germany, Greece, Spain, France, Italy, Austria, Hungary and Poland said that the European Union should stick to its core principles during the Brexit negotiations, which began on Monday.
In carefully choreographed talks that even saw the two men exchange mountaineering gifts, they agreed to discuss divorce issues before negotiations on a future trade deal can start.
Both EU negotiator Michel Barnier and his British counterpart David Davis said after the first negotiating session they were confident of quick progress but said major challenges lay ahead to meet the deadline of March 2019 for Britain to officially leave the bloc.
European Union officials had earlier warned May not to make that offer so early in the talks.
Austrian Foreign Minister Sebastian Kurz said: "If we don't succeed, both sides will lose". Our aim is to have one week of negotiations every month.
The Mechanical Engineering Industry Association, known by its German initials VDMA, says that that goal of the two-year negotiating process is "damage limitation" because Brexit won't benefit either side.
He had previously said not settling both elements simultaneously would be "the row of the summer".
Both sides acknowledged the clock was ticking, with the date for the UK's departure from the European Union fixed for March 2019. We also agreed on how we will structure our talks.
"It's not when it starts it's how it finishes that matters", he said.
The task facing Brexit Secretary David Davis is vast.
Frenchman Barnier struck a firm tone as he said the timetable for Britain's divorce after four troubled decades of membership made sense.
"It's not about punishment, it is not about revenge".
This move will discourage any other European Union member from leaving.
"And the consequences are substantial".
The EU is determined to have the final say on any Brexit deal. "But the 27 of us will formulate our interests very clearly and hopefully, together", Merkel said. "In addition, a dialogue on Ireland / Northern Ireland has been launched under the authority of the Coordinators". "We agreed on organisation and we agreed on priorities for the negotiation".
With these tight negotiations and UK's current domestic crisis it does appear that today will be the start of a very long and arduous 21 months, if not longer. It is up to us to make a success in a new political age.
The talks will be in English and French, they said in a joint statement.
UK Prime Minister Theresa May has said that the European Union referendum vote, which took place in June 2016, was also a vote for Britain to control its borders.
Ian Howells, Honda's European senior vice president, told an autos conference that the company had discovered more complexity and cost as it delved further into the impact an exit from the customs union would have on the British vehicle industry.
"In the meantime, the United States is committed to continuing discussions for improving trade and investment and coordinating on addressing global excess capacity issues".
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Once I started to get into a rhythm I was able to keep him a bit further away from the baseline and that made a big difference". Nishikori has won just two of 10 matches against Murray , but can't remember beating the British player at the U.S.