He will come back to Brussels on Thursday for more talks with Barnier and a news conference.
They then left the podiums without answering any questions from the fathering media, with the Frenchman saying the pair needed to work to which the Brexit secretary replied: "Work, yes that's right - work".
The British and EU Brexit negotiators met on Monday, pledging to "get down to work" in a first full round of talks on Britain's divorce terms from the European Union.
The Brexit Secretary is hoping to win round Michel Barnier over Britain's plan to guarantee the future rights of European nationals living in the United Kingdom amid deep divisions back home.
Yet defining the role of the ECJ will be one of the most sensitive issues of the Brexit divorce treaty, as Theresa May has vowed to take the United Kingdom out of the jurisdiction of the Luxembourg court.
But in the same interview, the Chancellor - seen as an advocate of a so-called soft Brexit - infuriated hardline Tory Brexiteers who want a clean break from the European Union by suggesting a transitional period could last two years.
Mr Davis is facing strong opposition from the EU over Britain's proposals for rights of European nationals living in the United Kingdom, as well as pressure to accept paying a huge "divorce" bill.
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Crucially, last month, Mr Davis caved in to the EU's insistence that the talks would move on to trade only when "enough progress" had been made on Brussels' three priorities.
'Protecting the rights of all our citizens is the priority for me going into this round and I'm clear that it's something we must make real progress on'. One said Hammond had urged against lifting pay restraints on what he called "overpaid" public sector workers, while another quoted the chancellor as saying driving modern trains was so easy that "even a woman can do it".
"I think on many fronts it would be helpful if my colleagues - all of us - focused on the job in hand".
The depth of division among Prime Minister Theresa May's ministers was highlighted over the weekend as Hammond was accused of using the Treasury to "frustrate" the Brexit process. UK's negotiating chief is expected to return to Brussels to wrap up the second round of talks and assess this negotiating week alongside Barnier at the Berlaymont press room.
The prime minister had made similar pronouncements before, but the statement to MPs and peers carried weight in Brussels. These two key players will meet regularly through the week, with the aim of keeping the talks on track.
British officials recently have also brought up the idea a transitional period after the March 2019 deadline to avoid a "cliff edge" scenario when it leaves the European Union, although the length and details have yet to be determined. "This government is facing a ticking clock over the Brexit negotiations", Hammond said on Sunday.