The negotiations are dealing with issues around Britain's divorce – Britain's exit bill, the rights of EU citizens living in Britain, and the Northern Ireland border.
The European Union and Britain offered few compromises at their first full round of Brexit talks which ended on Thursday, and the pound fell on worries that British ministers were prepared to walk away without a divorce deal.
While negotiators laid out their disagreements in Brussels, Prime Minister Theresa May met company bosses at home, with one employers' group saying her government needed to engage in "sustained and structured" discussions with business over Brexit and avoid an abrupt departure from the bloc.
Separately, academics warned of "widespread, damaging and pervasive" costs if Britain failed to reach at least a transitional trade deal with the EU before its scheduled departure from the bloc less than two years from now.
At the European Commission, the negotiators laid out their opening positions in four days of talks that confirmed some common ground.
But they also confirmed differences on how to protect the future of expatriate citizens, while uncertainty persisted over a financial settlement and the future of the intra-Irish border -- which will become an external frontier for the EU in 2019.
Chief EU negotiator Michel Barnier said there was "a fundamental divergence" on how to protect the rights of EU citizens living in Britain and of Britons in the remaining 27 EU countries after Brexit.
He said European courts should guarantee citizens' rights after Brexit.
"Any reference to European rights imply their oversight by the Court of Justice of the European Union," he told a joint news conference with British Brexit Secretary David Davis.
Britain, however, says people voted in last year's Brexit referendum to end shared EU sovereignty, and its judges should, therefore, have jurisdiction.
Barnier also called for more clarity on the British position on the financial settlement. Brussels says London must pay a share of the money the EU committed to spending when Britain was a member. The EU executive has floated a ballpark figure of around 60 billion euros ($70 billion).
Davis said the meetings in Brussels had provided "a lot to be positive about". But when asked whether Britain would accept the principle of a net payment from London to Brussels – and not vice versa as some British ministers have suggested – he gave no direct answer.
Barnier called on Britain to clarify at the next round of talks in August how it would maintain a common travel area with Ireland, which will remain in the EU.
Both sides have said they want to avoid re-imposition of border controls between the republic and British-ruled Northern Ireland. However, so far neither has proposed a solution to an issue that remains sensitive almost two decades after a peace deal ended years of violence in the province.
British international trade minister Liam Fox said a trade deal with the EU should be "one of the easiest in human history" to reach, although his country could manage without one if necessary.
Fox, a eurosceptic who campaigned for Brexit last year, said a trade deal should be simple because the two sides already have similar regulatory rules and no tariffs.
"The only reason that we wouldn't come to a free and open agreement is because politics gets in the way of economics," he told BBC radio in an interview.
But he added that Britain could survive without a deal, in comments that contrast to finance minister Philip Hammond, who has said that not reaching an agreement with the largest trading bloc in the world would be a "very, very bad outcome."
In Brussels, Davis played down talk of no agreement, saying that while Britain would never accept a "punishment deal", he saw no reason to think the EU would try to push such an outcome.