Both sides, however, avoided the vitriol that has sometimes marked years of the tortuous Brexit talks. They laid out plans to intensify their negotiations and pleaded for political support from their leaders when they assess the situation later in June.
Britain left the EU in January. Their relationship is now governed by a transition arrangement that keeps previous rules in place while they negotiate new terms. That expires at the end of this year unless they agree by this month to extend it, which Britain has repeatedly said it will not do.
So far, negotiations have not gone well.
"This week, there have been no significant areas of progress... We cannot go on like this forever," EU chief negotiator Michel Barnier told a news conference on Friday.
He said the EU and Britain remained far apart on the issues of fair competition guarantees and the governance of their new relationship, as well as fishing rights.
He noted some progress in talks over human rights guarantees that would allow Britain and the EU to go on cooperating in criminal and judicial matters from 2021, but the two sides were still far from agreement.
Britain had a similar message.
"Progress remains limited but our talks have been positive in tone," Britain's chief negotiator, David Frost, said. "Negotiations will continue and we remain committed to a successful outcome."