"I am not hearing any whistling, just the clock ticking," France's Barnier told a news conference when asked about Johnson's comments on the money the European Union expects Britain to pay when withdrawing.
Barnier also urged Britain to send Brussels its negotiating position on all key issues ahead of the second round of formal Brexit talks with his British counterpart David Davis, which start Monday in Brussels.
"On the single financial settlement, it is essential that the UK recognise the existence of financial obligations which are simply a result of the period in which they were members of the EU," he said.
Only then could the EU and Britain work on the "methodology" of how that bill would be worked out, added Barnier, a former European Commissioner and French foreign minister.
The EU says it will only start discussing future relations with the UK, including a possible trade deal, after "sufficient progress" has been made on those topics, hopefully later this year.
But the exit bill has been a major source of contention, with Johnson saying it was excessive in a speech to parliament on Monday.
"I think that the sums that I have seen that they propose to demand from this country seem to me to be extortionate and I think 'to go whistle' is an entirely appropriate expression."
"How do you build a relationship which is going to last with a country where you don't have trust?" said the Frenchman.
"I can't imagine that a very great country like the UK will not also be a responsible country and respect its commitments."
A British government official said in response to Barnier's comments that "when we leave the EU, the days of paying vast sums into the EU every year will end".
But Britain "recognised that we will need to discuss how we determine a fair settlement of the UK's rights and obligations as a parting member state."
Barnier repeatedly said that the "clock is ticking" before his deadline of October 2018 to reach the outline of a deal, before Britain formally leaves the EU in March 2019.
"We now need to know the UK's position on each of these issues in order to make progress," he said.
He insisted that he and his team were ready to work evenings, weekends "and even Bastille Day (the French national holiday which falls on Friday)" to respond if Britain manages to get its proposals in before Monday.
Barnier rejected May's offer at an EU summit last month on the rights of EU citizens after Brexit, saying that "the British position does not allow those persons concerned to live their lives as they do today."
He also insisted that the European Court of Justice (ECJ) should have jurisdiction over their fate in future, dismissing May's proposal that it should be under the control of British courts.
The European Parliament's Brexit chief, Guy Verhofstadt, said that Britain cannot stay a member of the EU nuclear regulator Euratom after Brexit.
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