The signatories say the "economic benefits" of the European Union single market, which allows free movement of goods, services, capital and people, and the customs union, which enables tariff-free trading within the EU, should be maintained until a final settlement between the United Kingdom and the EU is "agreed and implemented".
Asked whether Mr Davis had shifted his position, a British official referred to a statement released by Mr Davis's ministry on Friday which repeated calls for the withdrawal terms and future relationship to be "agreed alongside each other".
The EU insists that only when "substantial progress" is made on all three will it be possible to engage in the other main strand of talks - on trade.
The EU says Britain must honour its contributions to the bloc's budget, which has already been agreed up to 2020, as well as commitments to development programmes for poorer member states. She also said: "I am equally clear that no deal for Britain is better than a bad deal for Britain".
Following tomorrow's meeting, talks will continue on a monthly basis throughout the summer.
"The fact they are coming and that they agree to talk about the subjects that we set out, shows that the clash is under control", a senior European official told AFP on condition of anonymity. "The withdrawal and future are intimately linked". We want to end the anxiety facing four million citizens.
"That has always been our first aim and that is what we will do", the spokesman said.
European Union officials suggested the apparent climbdown could buy May's unstable government breathing space to actually decide what kind of future relationship it wants.
Meanwhile a separate row erupted with Brussels, after the Brexit department strenuously denied reports it will settle a multi-billion pound "divorce bill" before starting talks on future trade deal with the EU.
Mrs May has promised MPs a "take it or leave it" vote on whether to accept the deal or take Britain out of the European Union without agreement and fall back on World Trade Organisation rules.
We now know that at precisely 11:00 BST on Monday morning, nearly exactly a year after the Brexit referendum, the all important exit negotiations will begin.
"We should be protecting jobs, protecting economic growth and protecting prosperity", he said in Luxembourg last week.
Speaking as he arrived for a meeting of European Union finance ministers in Luxembourg, he said: "As we go into that negotiation, my clear view - and I believe the view of the majority of people in Britain - is that we should prioritise protecting jobs, protecting economic growth and protecting prosperity as we enter those negotiations and take them forward".
And the source told the BBC that it was understood the talks would broadly follow the EU's preferred sequence, dealing with issues of citizens' rights and a framework for calculating outstanding financial liabilities before moving on, possibly later in the year, to deal with the UK's future relationship with the EU.