"Our objective is clear, we must first tackle uncertainties caused by Brexit", he told reporters.
David Davis and Michel Barnier make a joint media address.
"We will do all that we can to ensure that we will deliver a deal that works in the best interest of all citizens", added Davis at the Berlaymont VIP corner. Brexit negotiators will discuss Monday Britain's financial obligations to the European Union as the long, complicated and potentially perilous process of the United Kingdom leaving the bloc finally gets underway. Mr Davis went into the talks announcing that he was in a "positive and constructive" frame of mind and that he was determined to build a "strong and special partnership" with the EU.
Macron, a committed pro-EU leader and ally of German Chancellor Angela Merkel, easily won French legislative elections on Sunday, cementing his power base.
UK Prime Minister Theresa May. "My personal view is we will see a result that will be fair ultimately for both sides because it's not within either sides' interest for it not to be fair".
SNP Europe spokesperson Stephen Gethins said: "We now have a Tory government consumed by chaos on every front and any attempts to avoid parliament and the public in order to simply carry on regardless with a smokescreen Brexit is outrageous and utterly unsustainable".
Britain is due to leave the European Union at midnight Brussels time (11pm in the UK) on March 29 2019 - unless an extension is agreed by all 27 remaining member states - with or without an agreement.
"The most important ask from business - nearly more important than what the end result looks like - is that we have a smooth path to get there".
May officially triggered the two-year Brexit process in March when she was riding high in the opinion polls.
The outcome of the UK's snap election on June 8 has substantially weakened Prime Minister Theresa May's hand in the upcoming negotiations.
Britain appears to have given in on the EU's insistence that the negotiationsfirst focus on three key divorce issues, before moving onto the future EU-UK relationship and a possible trade deal.
Other issues on the agenda, at least in the near term, include establishing residential rights of more than 3 million European Union citizens now living in the United Kingdom - and the 1 million British expats living in European Union member states - once the formal exit is complete.
A Survation poll for ITV's Good Morning Britain programme put the opposition Labour party ahead by three points (44% to 41%), but also showed that 52% believed May was the best person to lead Brexit negotiations.
"The best way we can spend this week is to rebuild trust", rather than tackle the big hard issues right at the start, another European source said. Priorities drawn up at the EU's insistenceThe two other priorities on the initial agenda - drawn up at the EU's insistence - are how to maintain a "soft" border between Northern Ireland and the Irish Republic after Brexit, and the UK's financial obligations to European institutions and programmes.
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.