Johnson has refused.
"With every day that passes, the chances of a timely agreement do start to fade," said Ursula von der Leyen, President of the European Commission, the EU executive.
In a speech to the European Parliament, she said the divorce agreement "cannot be unilaterally changed, disregarded or dis-applied".
"This is a matter of law, trust and good faith ... Trust is the foundation of any strong partnership," she said.
The British pound, which moves in line with perceptions of either a chaotic or orderly Brexit, held within striking distance of a two-month low on Wednesday.
The EU fears a disorderly Brexit if the terms of the trade relationship are not agreed, and former British prime ministers have said breaking the law is a step too far that undermines the country's image.
Johnson said it was essential to counter "absurd" threats from Brussels including that London be required to put up trade barriers between Britain and its province of Northern Ireland and that the EU would impose a food blockade. Such steps, he said, would threaten the unity of the United Kingdom.
The Internal Market Bill is being debated by the British parliament, where Johnson faces opposition from some members of his governing Conservative Party.
Justice Secretary Robert Buckland said the government sees a 'way through' the parliamentary maze, and Johnson has been talking to the party rebels.
Buckland said there had been talks with Bob Neill, a Conservative lawmaker who has proposed amending the bill to ensure that any attempt to use the clauses that breach the Brexit divorce agreement receive prior approval from parliament.
Britain's Northern Ireland minister Brandon Lewis told parliament he stood by remarks he made last week that the bill would "break international law in a very specific and limited way".
But Scotland's top law adviser to the British government, Richard Keen, has offered his resignation to Johnson over his plan to break international law, the BBC reported on Wednesday.
EU diplomatic sources told Reuters that if the bill was passed in its current form, Brussels felt it could not deal with London.
(Additional reporting by Kate Holton, William James and Andy Bruce, Editing by Timothy Heritage and Kevin Liffey) ((email@example.com; 07825218698;))