The EU has threatened the UK with legal action over moves to override key parts of the Brexit divorce deal.
In a statement following emergency talks between the two sides, the EU said the changes "seriously damaged trust between the EU and the UK".
The UK government said its Parliament is sovereign and can pass laws which breach the UK's treaty obligations.
Meanwhile, trade talks between the UK's Brexit negotiator Lord Frost and his EU counterpart Michel Barnier continue.
The source of the EU's concern is Mr Johnson's proposed Internal Market Bill, which was published on Wednesday.
It addresses the Northern Ireland Protocol - an element of the withdrawal agreement designed to prevent a hard border returning to the island of Ireland.
The bill proposes no new checks on goods moving from Northern Ireland to Great Britain. It gives UK ministers powers to modify or "disapply" rules relating to the movement of goods that will come into force from 1 January, if the UK and EU are unable to strike a trade deal.
Mr Johnson has defended the bill, saying it would "ensure the integrity of the UK internal market" and hand power to Scotland and Wales, while protecting the Northern Ireland peace process.
But critics - including a growing number of Conservative MPs - say the move will damage the UK's international reputation after a minister admitted the plans break international law.
European Commission president Ursula von der Leyen said she was "very concerned" following the tabling of the bill in Parliament, and that such actions "undermine trust" with the EU.
Labour leader Sir Keir Starmer urged the government to consider "the reputational risk that it's taking in the proposed way forward".
Legal analysis circulated among EU member states found that the Internal Market Bill would breach the Brexit deal and could "open the way" for the EU to take legal action against the UK.
But EU lawyers say it is unlikely a case could be launched before the end of the year.
The meeting of the UK-EU Joint Committee, co-chaired by Mr Gove and Mr Sefcovic, was held in London but was also attended over video link by Northern Ireland's First Minister and Deputy First Minister Arlene Foster and Michelle O'Neill.