The two negotiators did not take questions, saying "they have to work" now.
Davis and Barnier spent only a half-hour in negotiations Monday, and photographs from the talks featured bulging files of papers on Barnier's side of the table and little evidence on Davis'.
Working groups will focus on three areas: citizens' rights; the EU demand that Britain pays some 60 billion euros ($70 billion) to cover ongoing EU budget commitments; and other loose ends, such as what happens to British goods in EU shops on Brexit Day.
Barnier and Davis last month agreed on a potential timetable for negotiations towards a future trade relationship, which Britain would like to start as soon as possible.
He pointed to four categories where they needed to make progress on: "The issue of citizens' rights, the issue of finance, of separation and of course, separately, Northern Ireland". The EU has publicized its preferred agenda, which includes the settlement of issues including citizens' rights and financial obligations, before discussions turn to trade agreements.
For now, the EU says May's offer to guarantee the rights of 3 million Europeans in Britain falls short.
Negotiations on the exit bill might be especially tough, following British Foreign Minister Boris Johnson's remark last week that the European Union could "go whistle" over its "extortionate" bill demand.
Prime Minister Theresa May, her authority diminished after losing her majority in a June election she did not need to call, has struggled to control rival cabinet ministers.
On Thursday, the British government introduced a draft law that would formally end Britain's European Union membership, as preparation for eventually divorcing the bloc and gaining back legislation power of parliaments. "I think my colleagues should be very quiet, stick to their own departmental duties and I think the public expects us to be disciplined and effective. This government is facing a ticking clock over the Brexit negotiations", Hammond said on Sunday. Or does he just have no ideas?
Did David Davis forget his notes?
At a brief press conference with Mr Barnier earlier in the morning, the Brexit secretary said that this week's talks would delve "into the substance of the matter", include discussions on Britain's European Union exit bill and citizens rights.
"David Davis has vowed to "get down to business" and hit the "substance" of Brexit talks as a new round kicks off today", wrote the Daily Mirror.