EU negotiator Michel Barnier said the UK had not been clear enough about where it stands on these issues and that was hampering progress.
UK Brexit Secretary David Davis said the negotiations on the so-called divorce bill had been “robust”.
He said progress had been made but both sides needed to show “flexibility”.
Mr Barnier said: “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 – and the other separation issues where this week’s experience has quite simply shown we make better progress where our respective positions are clear.”
He 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 European Court of Justice – something Prime Minister Theresa May has ruled out.
There was also disagreement over “the rights of future family members” – meaning children born in the future to EU citizens in the UK – and “the exports of certain social benefits”, he added.
Mr Davis said the UK had published its approach to citizens’ rights since the first round of negotiations, which he described as “both a fair and serious offer” and had now published a joint paper setting out areas of agreement, and issues for further talks.
Sticking points included the rights of employees of EU-based companies to work for extended periods in other countries and the right of EU citizens to vote in UK local elections.
Mr Davis also rejected the idea that there was a lack of clarity from his team on Northern Ireland, saying the two sides had discussed ways of “achieving a flexible and imaginative solution to address the unique circumstances around the border” and preserve the common travel area.
Mr Barnier said: “I know one has to compromise in negotiations but we are not there yet. When I say, and I think I was very clear and transparent about that, that there are things that are inseparable from others. That’s the financial settlement.
“Let’s be very clear. We want clarity on that because we need to be able work more until we come to areas of compromise.”
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.”
And he added: “We have had robust but constructive talks this week. 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.”
Mr Davis also told the news conference in Brussels that Britain could “make it work” if it had to walk away from a “punishment” trade deal with the EU, but added: “Nobody expects a punishment deal. Michel and I are going for a good deal.”
UK Foreign Secretary Boris Johnson has said the EU can “go whistle” if it demands an “extortionate” payment but other ministers have struck a more conciliatory tone. Sources have suggested to the BBC the bill could be between 30 and 50 billion euros.
Labour’s shadow Brexit secretary Sir Keir Starmer the “lack of progress” on issues such as the rights of EU citizens in the UK and UK citizens in Europe was “deeply concerning” and would cause “anxiety for millions of families”.
He questioned whether phase two of the talks could get under way in October as planned, something that would “trigger deep concern for businesses and communities across the UK”.
“The reality is that we have a government that is unprepared, divided and incapable of securing a good deal for Britain. We urgently need a fresh approach,” he added.
The EU has said talks won’t move on to the subject of future trading arrangements until it judges there’s been adequate progress on the separation issues.
The two sides are meeting for four days each month, with this week’s talks aimed at scoping out points of difference and common ground in those areas that have been identified as requiring urgent attention.
Meanwhile, the UK government has announced that MPs are set to debate the repeal bill – a key piece of Brexit legislation that will transform EU laws into British laws – for two days from 7 September.