The EU threatened legal action if parts of the contentious bill, which a UK government minister admitted broke international law, were not removed.
A controversial Brexit bill that could override parts of the Withdrawal Agreement signed with the EU has passed its latest stage in the UK's House of Commons after a compromise was struck with Conservative MPs.
MPs backed the government's UK Internal Market Bill on Tuesday night, which will be voted on again next week before being scrutinised by the House of Lords, the UK parliament's upper chamber.
A potential rebellion of Tory MPs was averted after the government promised the Commons would have a say before the new powers in the bill were used.
The legislation, which has caused an outcry in the EU and at home, could see the government renege on commitments relating to Northern Ireland it signed up to under a year ago.
Former UK Prime Minister Theresa May repeated her criticism of the bill this week, warning that it would do "untold damage" to the UK and accusing Boris Johnson's government of acting "recklessly and irresponsibly".
Around 30 Tory MPs abstained in the first parliamentary vote on the bill last week after a government minister admitted it would break international law.
Brandon Lewis, the Northern Ireland Secretary, told MPs that the bill "does break international law in a very specific and limited way".
The legislation, which the government described as a "safety net," was also widely criticised by opposition MPs and the EU, which has threatened legal action if contentious sections of the bill were not amended or removed.
European Commission President Ursula von der Leyen said last week that she was "very concerned," tweeting that the move would "break international law and undermine trust".
The bill seeks to ensure an unimpeded flow of goods and services across the borders of the UK's four nations, overriding provisions made for Northern Ireland which were negotiated and ratified in the binding Withdrawal Agreement signed with the EU.
Under the deal, Northern Ireland is obliged to follow some EU rules after the end of the post-Brexit transition period, maintaining an open border with between the north and south of Ireland. after the UK leaves the EU's Single Market and Customs Union.
Prime Minister Boris Johnson said the new law would protect the Good Friday Agreement, the peace deal signed in 1998 which brought the Troubles in Northern Ireland to an end.
"This UK internal market bill is about protecting jobs, protecting growth, ensuring the fluidity and safety of our UK internal market and prosperity throughout the United Kingdom," Johnson added.
The EU's chief negotiator Michel Barnier came to London on Wednesday for informal discussions, ahead of formal post-Brexit trade talks which are due to resume on September 28.
As EU ministers met in Brussels on Tuesday, Germany's Minister of State for Europe Michael Roth urged the British government to "stop the games".
"We are really really disappointed about the results of the negotiations so far. This so-called internal market bill extremely worries us, because it violates the guiding principles of the withdrawal agreement, and that is totally unacceptable for us," he added.
The EU divorce deal renegotiated by Boris Johnson in October 2019 contributed to the re-election of his Conservative government, and paved the way for the UK's delayed exit from the bloc last January.