Theresa May has said both the UK and EU want to work towards a future Brexit deal “at a faster pace”, after being warned that time is running out.
Arriving at an EU summit, the prime minister said “very good progress” had been made on a withdrawal agreement.
The PM will brief 27 other EU leaders for the last time before October, when both sides hope a deal will be done on the UK’s March 2019 departure.
But Irish leader Leo Varadkar said the lack of progress was “disappointing”.
He said he expected fellow leaders to send a “strong message” to Mrs May that talks had to “intensify”.
The prime minister, who has been under unrelenting pressure at home within her own party, has called her cabinet together for what has been billed as a make-or-break meeting at Chequers on 6 July to agree the UK’s blueprint for its future relations with the EU.
Arriving in Brussels, Mrs May said she was looking forward to “securing our strong future partnership” which she said was in the interests of both the EU and UK .
“I think both sides are keen to continue that work at a faster pace than we have done up till now and certainly we would welcome that.”
She added that the UK would publish a White Paper setting out “in more detail what strong partnership the United Kingdom wants to see with the European Union in the future”.
Mrs May said it was in everyone’s interests that a new partnership be agreed, adding: “That’s why I’m confident we can sit down and discuss that at pace and ensure that we can achieve what we want, which is that continuing partnership with the European Union on economic and security matters.”
European Commission President Jean-Claude Juncker agreed he was “worried” about a lack of progress but said he would not “lecture” Mrs May.
Asked if talks could end in no deal, he added: “We are preparing for different scenarios – on the proper withdrawal agreement but, in parallel, we are working on the no deal.”
Cabinet divisions over the UK’s customs arrangements after December 2020, when the transition period agreed with the EU is due to end, have yet to be resolved, as have arguments over the future movement of goods and people across the border between Northern Ireland and the Republic of Ireland.
Mrs May’s former top aide, Nick Timothy, has urged her to face down her opponents in the cabinet, telling the Daily Telegraph the “time for playing nice and being exploited are over”.
With less than nine months to go before the UK’s scheduled exit, leading businesses have said the time has come for clarity and issued warnings about the impact on jobs of leaving the EU without an agreement.
The prime minister will hold a number of face-to-face meetings with European counterparts on day one of the two-day summit, the main focus of which will be on the migration challenges facing Europe and eurozone reform.
The remaining 27 EU leaders will discuss Brexit on their own on Friday morning, by which point Mrs May is expected to have left Brussels.
On the eve of the summit, Mr Varadkar said he wanted “detailed proposals” from the UK on how it would honour the “clear commitments” made in December about the Irish border and citizens’ rights.
Persuasion, not detail
By the BBC’s political editor Laura Kuenssberg
There is no expectation that the prime minister will arrive in Brussels with a magic key to unlock the Brexit process.
But Theresa May heads to the Belgian capital later with a promise at least that within 10 days she will have been able to persuade her cabinet to agree more of the UK’s vision for life outside the EU.
And that she will be able to put a detailed and ambitious vision into words in a White Paper to be published not long after – the UK’s blueprint of how trade, customs, agriculture, and so many other areas might work after Brexit.
That, she hopes, in mid-July will usher in a genuine discussion about the long-term relationship between the country and the rest of the continent.
This summit therefore is not about technical negotiations, but about promises and persuasion, for the prime minister to convey that she is in charge of her agenda.
“Time is running out for the Withdrawal Agreement to be concluded satisfactorily by the October European Council,” he said.
“I expect EU leaders to send a strong message to the UK that negotiations with the taskforce need to intensify.”
The EU’s negotiator Michel Barnier has said “serious divergences” remain over the question of backstop arrangements for the Irish border if neither of the UK’s proposed customs proposals are deemed workable.
Elsewhere, Mrs May will seek to show solidarity with the rest of Europe in their efforts to deal with illegal migrant flows across the Mediterranean from Africa and the Middle East.
The issue has divided Europe for more than two years but tensions have increased since the election of a populist government in Italy, which has pledged to crack down on unlawful migration, and growing political uncertainty in Germany amid a backlash against Chancellor Angela Merkel’s immigration policies.
Mrs May is expected to stress the need to tackle the problem of people smuggling at its source, citing the success of a project in Nigeria where once the dangers of crossing the Mediterranean were explained to people, their attitudes to illegal working in the UK changed.
On security, the prime minister will call for collective action against misinformation, cyber warfare and money laundering by “hostile states” such as Russia. One example of this, she will say, is the UK’s sharing of details of Russian intelligence officers expelled after the attacks on Sergei and Yulia Skripal in Salisbury with EU allies.
The working dinner will coincide with England’s final World Cup group game against Belgium, whose prime minister Charles Michel will also be present.
The UK’s permanent representative in Brussels couldn’t say how much of the match Mrs May, who on Wednesday ordered St George’s flags to be flown above No 10 for remaining England games, would see.