The Brexit Secretary hit out at the EU's chief negotiator as he described reports that Britain is willing to pay a £50bn divorce bill as "nonsense".
Mr Barnier took a swipe at British negotiators at the end of the last round of talks in Brussels last week.
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He said they had failed to make "sufficient progress" on the exit payment, the Irish border and citizens' rights to allow the discussions to move onto the UK's future relationship with the EU.
A clearly-angry Mr Davis took aim at Mr Barnier while appearing on the BBC's Andrew Marr Show. He said: "(Barnier) can take any line he likes on the way we conduct our negotiations - that's up to us, not up to him."
He added: "That's the point about the Europeans. They won't talk about the future. They'll only talk about so-called divorce proceedings."
Mr Davis went on condemn Mr Barnier personally, but then backtracked by insisting he had been talking about the European Commission as a whole.
He said: "Of course he wants to put pressure on us, which is why the stance this week in the press conference - bluntly, I think it looked a bit silly, because there plainly were things that we achieved."
The Brexit Secretary also urged potential Tory rebels to back the Government's EU Withdrawal Bill when it comes before the Commons this week.
First Secretary of State Damian Green has warned that backbenchers who fail to support the legislation risked letting Jeremy Corbyn into Downing Street.
But Mr Davis said: "This bill is about ensuring continuity. Anybody - Remainer or Leaver - should support this bill."
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