Michael Gove travelled to Brussels on Monday morning ahead of another week of Brexit trade talks in the EU capital.
The cabinet minister is representing the UK government at so-called "joint committee" talks about the Northern Irish border – which is still a source of disagreement in negotiations.
Mr Gove is meeting with European Commission vice president Marcos Sefcovic, who has accused the UK government of moving towards an "extremely serious violation" of the Brexit withdrawal agreement signed earlier this year.
Ministers have admitted that their internal market bill is a breach of international law and overwrites part of the Brexit divorce deal.
But they say that without the legislation the agreement Boris Johnson signed up to earlier this year could result in checks and controls on goods between Northern Ireland and the rest of the UK.
Despite this being clear from the text of the agreement at the time it was signed, the UK now says it would not be acceptable and wants the EU to agreed to waive some controls that would be imposed across the Irish Sea.
Also this week, Lord Frost, the UK's chief negotiator, will continue parallel talks to try and strike a separate free trade agreement, which needs to be in place by the end of the year to avoid a no-deal.
Subjects to be discussed include regulatory alignment, fisheries, and governance of any deal – key sticking points so far on which little progress has been made. Negotiators will also consider trade in services and law enforcement cooperation, as well as the possibility of civil nuclear cooperation.
Downing Street briefed Tory-supporting newspapers at the end of last week that a deal is in sight, but there is no concrete sign of this so far in Brussels.
The European Commission says Michel Barnier, its chief negotiator, is neither optimistic nor pessimistic, but determined to reach a deal.
A UK government spokesperson said: "We are looking forward to continuing our discussions at the Joint committee and working towards a satisfactory outcome for both sides."