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.
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.
As doubt for and objection to Brexit continue, progress favorable to those in support of the breaking away has been made, creating a silver lining for the closely watched second round of talks. Diplomats had feared a collapse in talks after the foreign secretary, Boris Johnson, caused confusion with his statement that the European Union should "go whistle" for the "extortionate" sums "they have demanded".
"For us, it's incredibly important we now make good progress", added Mr Davis, who held a first day of talks a month ago to agree an agenda, a year after Britons vote to leave the EU.
Barnier has dismissed the British rights offer as falling short of the European Union demand that its 3 million citizens there keep all their existing rights for life and have recourse to the European Union courts to enforce those rights even after Britain has left.
European diplomats fear the United Kingdom is continuing to box itself into an uncompromising position and are expecting it to push back strongly on the court, as both sides map out their differences in detail during the negotiations.
But Brussels insists it will only start discussing the future once there has been "sufficient progress" on key issues involved in Britain's withdrawal―an estimated 100-billion-euro ($112 billion) exit bill, citizens rights, and the border in Northern Ireland.
And his allies blasted Michael Gove for reportedly being behind the "smear campaign" of leaking details from last week's Cabinet meeting. 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".
"We'll now delve into the heart of the matter", Barnier, a former French foreign minister and European Commissioner, told reporters.
"I think on many fronts it would be helpful if my colleagues - all of us - focused on the job in hand".
Asked why colleagues are "going for you", he pointed to disputes over Brexit, saying: "Some of the noise is generated by people who are not happy with the agenda that I have".
Discussions on the politically charged issue of the Irish border issue will be led by Sabine Weyand, Barnier's deputy, and Olly Robbins, permanent secretary of the department for exiting the EU.
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.