But Belgium Prime Minister Charles Michel, who argues for a need to protect European Union integration from British ambivalence toward the project, tweeted: "It's time for action and certainty".
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.
Brexit negotiations about the terms of leaving the bloc began on Monday but Mr Tusk addressed the prospect of Britain reversing its decision, quoting a line from the 1971 song Imagine: "So, who knows - "You may say I'm a dreamer, but I'm not the only one".
"I hope that in this area we can also have a Europe that is open to free trade and our values, but that protects when others do not respect certain rules".
"For me the shaping of the future of the 27 is a priority coming before the issue of the negotiations with Britain on the exit", Merkel said.
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Outlining the five main principles of her "fair and serious offer", May told other European Union leaders at a summit in Brussels that she wanted to offer certainty to European Union citizens about their future in Britain, again using a softer tone in her approach to Brexit. "Not for dreams and uncertainty", the Belgian premier tweeted in response to Tusk.
He said: "Because she has taken the action that she has, she has bought herself a lot of time".
Germany's Europe minister, Michael Roth, said in Luxembourg that the opening of the negotiations had shown British leaders still needed a "reality check" on what they could achieve.
Theresa May is on "probation" as Prime Minister, a Tory MP has claimed.
These comments were underpinned by Bank of England governor Mark Carney, who said in a speech at Mansion House on Tuesday it was not the time for higher interest rates.
European Union officials and diplomats greeted the agreement of Brexit Secretary Davis to a format and sequencing of talks that had been proposed by Barnier as sign that British Prime Minister Theresa May's weakened and potentially divided government was bending to Brussels' insistence on how negotiations will work. The EU thinks the Luxembourg court should be the arbiter of disputes over citizens' rights, an idea that is toxic to Tory backbenchers - though cabinet ministers have struck a markedly less combative tone on Brexit since the general election wiped out the Conservatives' majority.
He said "we are witnessing the return of the European Union rather as a solution, not a problem".