"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.
German Chancellor Angela Merkel says she hopes for a "good agreement" after Brexit talks in which 27 European Union countries will listen carefully to what Britain wants but also defend their own interests.
This breaking news story is being updated as more information emerges - please refresh the page for the most recent version. "And fair means that we want to keep the British as close as possible to the European Union - but never at the price that we divide the remaining 27 European Union states".
Almost a year to the day since Britons shocked themselves and their neighbours by voting on 23 June to cut loose from their main trading partner, and nearly three months since Prime Minister Theresa May locked them into a two-year countdown to Brexit in March 2019, almost nothing about the future is clear.
"We must first tackle uncertainties caused by Brexit".
The other major story on Monday morning is a "potential terrorist attack" in North London, where a van was driven into a crowd outside a mosque in the early hours of the morning. European Union negotiators need no longer be as anxious that Britain's departure might inspire others to follow.
Talks with the European Commission's chief negotiator Michel Barnier will focus on the status of expats, the UK's "divorce bill" and the Northern Ireland border. "A deal like no other in history", Brexit Secretary David Davissaid in a statement as he headed into the talks.
May, under pressure after losing her ruling Conservatives' majority in a botched snap election and over her response to a devastating fire that killed at least 58 in a London apartment block, says she wants a clean break with the European Union - a strategy some in her party have challenged as risking economic growth.
Mr Davis - who earlier said that he was hoping to negotiate a "deal like no other in history" - said that the United Kingdom was looking for "a new, deep and special partnership with the EU". Both sides want transparency to be the default.
From his comments, it appeared that the Brexit talks will largely follow the EU's conditions and will center on the two sides' new relationship only once sufficient progress has been made on the withdrawal issues.
The smiles belied the fact that at stake is not just Britain's future but also Europe's postwar political order and its place in the world, which could be fatally undermined without an agreement by the March 2019 deadline. The election of the fervently Europhile Macron, and his party's sweep of the French parliament on Sunday, has revived optimism in Brussels.
Anxious by immigration and loss of sovereignty, Britain previous year voted to end its decades-old membership of the 28-country bloc - the first state ever to do so - in a shock referendum result.
Business leaders have already warned against such a "cliff edge" scenario and are eager to see a transitional period to give them time to adjust after the split.
Monday's talks however are likely to focus on the practical details of timings for the coming months, with the big, divisive issues left aside for now, officials said.