However, the Brexit Secretary said the United Kingdom would meet its obligations but would not be drawn on a financial figure.
Trade minister Greg Hands echoed Mr Davis' views on the progress of Brexit talks.
Meanwhile Mr Barnier claimed he needed to educate the United Kingdom about the price it would pay for leaving the bloc.
Barnier was speaking at a tense press conference alongside the UK's Brexit Minister David Davis at the end of the third round of EU-UK negotiations in Brussels in the headquarters of the European Commission.
He dismissed newspaper reports the United Kingdom had secretly agreed to pay a figure of up to £50bn as "nonsense".
THE UK'S BREXIT negotiator David Davis has said that the bill the UK must pay upon leaving the European Union is what "frightens them the most".
"I think there is frustration that we have not been able to get on that longer-term issue, that we're stuck on this separation issue, and we're not able to get on to the issues that will matter in the longer term for the future prosperity of the United Kingdom and the people of Europe", he said.
Mr Davis said money was "the thing that frightens them most" and insisted that the United Kingdom would not be forced into backing down in order to begin trade talks in October.
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"We're going through this very systematically, very British way, very pragmatic way of doing it and of course he's finding it hard, which is why this stance in the press conference", he added. "They are trying to use time against us". "It takes the laws that are there now and puts them in place the day after we leave".
Foreign Secretary Boris Johnson said some of the figures touted for the size of the divorce bill were "extravagant" and the United Kingdom would only respect a number that was "serious and validated in law".
"We are a country that meets its worldwide obligations - but they have got to be there", he said.
The continuing tit-for-tat between the two sides comes as Downing Street called for unity among its MPs as they prepare to debate the government's flagship Brexit bill.
But Mr Davis said Labour was onto its "perhaps seventh, eighth, ninth" policy on Brexit and the opposition knew the legislation was essential to ensuring legal certainty and practical continuity as the United Kingdom takes responsibility for policy in a wide range of areas.
The EU Withdrawal Bill will repeal the law that paved the way for the United Kingdom to join the European Economic Community in the 1970s and convert 40 years worth of EU statutes into domestic law.
No 10 has told would-be Conservative rebels, most of whom favour a soft Brexit, that they risk allowing Labour and Jeremy Corbyn to capitalise if they block the bill's passage through the House of Commons. Labour also said last month that it wants Britain to remain in the single market and customs union for as many as four years after exiting the EU.
The Brexit Secretary dismissed as "nonsense" claims that the United Kingdom would pay a £50 billion fee to exit the EU.