The Brexit Secretary refused to say the UK was prepared to put more money on the table straightaway – instead insisting there could not be a “nothing-for-nothing” offer.
And he appeared to single out Germany and France for refusing to compromise, arguing other EU countries were eager to move the negotiations on to discussing future trade.
“Many of them do want to move on. They see it’s very important to them,” Mr Davis said, speaking in Berlin.
“Countries like Denmark, countries like Holland, countries like Italy and Spain, countries like Poland can see the big, big benefits in the future deal we are talking about.”
He added: “Germany and France, it’s an open secret of Europe – they are the most powerful players on the European continent. Of course they are.
“What they believe is very influential, sometimes decisively so. But it’s the whole-of-Europe decision, it’s a 27-country decision.”
Michel Barnier, the EU’s Brexit negotiator, said Britain must budge by next Friday, but Mr Davis said: “So far in this negotiation we have made quite a lot of compromises.”
The comments may provoke a backlash in EU capitals, where heads of state have insisted they are united in a belief the UK must agree withdrawal terms - including the financial settlement - before the talks can progress.
They come before Theresa May meets the Irish Prime Minister, Leo Varadkar - to discuss the future Irish border, another key withdrawal controversy - and EU Council President Donald Tusk, at a summit in Sweden.
Arriving in Gothenburg, Mr Varadkar made clear the EU would not shift its position, saying: “If we have to wait until the New Year, we have to wait for further concessions, so be it.”
Mr Davis, speaking to BBC Radio 4’s Today programme, also hinted that the Prime Minister is set to U-turn on her plan to put the precise Brexit date – 11pm on 29 March, 2019 – in domestic law.
Up to 20 Tory backbenchers are poised to rebel, fearing the move will make it impossible for Parliament to force a delay, to prevent a no-deal exit, if no agreement can be reached.
Mr Davis praised the proposal, but hinted at a climbdown, saying: “How it’s done, what form it is – I’m not going to pre-empt that. We will debate it and we will see how it goes.”
He was also asked who gave him more trouble – EU leaders, or Tory backbenchers – replying: “I’m not going to answer that – I think it varies day by day.”
Mr Davis spoke after using a conference in the German capital to urge its leaders not to “put politics above prosperity”, throwing obstacles in the way of an agreement.
The warning raised eyebrows because EU countries see Brexit as a stark example of the UK doing exactly that.
EU sources suggested Mr Tusk will tell Ms May that, it could not be taken for granted that leaders will agree to move on to the second phase of the talks, at a summit next month.
One said: “Mr Tusk will inform Mrs May that such a positive scenario is not a given, it will require more work and that time is short.
“And he will ask Mrs May how the UK plans to progress on the three key issues for phase one.”
The three issues where “sufficient progress” must be made are the financial settlement, citizens' rights and the border between Northern Ireland and Ireland.
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