The UK and Brussels have "fundamental" disagreements over citizens' rights, the EU's chief Brexit negotiator has said.
Michel Barnier also insisted there must be "clarification" on Britain's position on a number of issues.
It follows the second set of four-day talks with Brexit Secretary David Davis on Britain's withdrawal from the European Union.
Speaking at a joint news conference, Mr Davis said talks had been "robust but constructive".
"Clearly, there's a lot left to talk about and further work before we can resolve this."
"Ultimately getting to a solution will require flexibility from both sides," he added.
Mr Barnier said there had been some areas of agreement about how Britons living abroad and EU nationals living in the UK should be treated after Brexit.
But he said Brussels believed citizens' rights should be backed by the Court of Justice of the European Union.
"There does remain one fundamental divergence on the way in which such rights would be guaranteed and on several other points, for example, the rights of future family members or the exports of certain social benefits."
The former French minister said the third round of talks "must be about clarification".
"We require this clarification on the financial settlement, on citizens' rights, on Ireland - with the two key points of the common travel area and the Good Friday Agreement."
"The other separation issues where this week's experience has quite simply shown we make better progress where our respective positions are clear," Mr Barnier added.
Mr Davis struck a more optimistic tone, and said: "Overall I'm encouraged by the progress we have made on understanding each other's positions."
Europe's chief negotiator also warned that all accounts "must be settled" when Britain leaves the bloc.
The so-called "divorce bill" to settle outstanding liabilities, could run to tens of billions of pounds, and has emerged as a key battleground in Brexit talks.
Both sides are hoping to reach agreement on the method of calculating the financial settlement by October's European Council summit.
Mr Davis said: "We both recognise the importance of sorting out the obligations we have to one another, both legally and in a spirit of mutual cooperation."
The negotiations have so far focused on so-called "phase one" issues of separation - including the financial settlement, citizens' rights, the Irish border and Britain's position in relation to Europe's civil nuclear regulator, Euratom.
Earlier this week, the European Commission dismissed criticism of David Davis for leaving Brexit talks after an hour-long meeting with Mr Barnier.
The Brexit Secretary was rounded on by opposition parties for leaving the four-day talks on Monday and for being photographed without any papers at the meeting, while Mr Barnier and his team had stacks of notes in front of them on the table.
The photograph led to claims Britain was unprepared for the talks amid a damaging Cabinet row apparently over the shape of Brexit at home.