European Union leaders were meeting Wednesday in a new 27-member format to agree a common response to Britain's decision to leave the bloc and discuss ways to bolster it thereafter, amid differences over how best to take the project forward.

In a sign of things to come, British Prime Minister David Cameron - who took part in a first day of summit talks on Tuesday - was not sitting in the Brussels meeting, after 51.9 per cent of British voters opted last week in favour of a so-called Brexit.

"I think it is not about him today. ... Today is about us, what we are going to do about our unity and about preparation for [the] transitional period for British withdrawal," Lithuanian President Dalia Grybauskaite said.

The 27 leaders are expected to issue a joint statement calling for Britain to trigger formal exit negotiations as soon as possible, an EU source said on condition of anonymity.

"The most important thing today is to agree a process and a launch to that process," the source added.

Once divorce proceedings are under way - a process not expected for several months - it will also pave the way for discussions on Britain's future relationship with the EU.

"We need more than ever a united Europe compared to a 'Disunited' Kingdom," said Luxembourg Prime Minister Xavier Bettel. Britain is officially known as the United Kingdom.

The referendum outcome has triggered a political crisis in Britain, as well as testing the country's unity after Scotland voted to remain in the EU, giving rise to calls for a new Scottish independence vote.

Scottish First Minister Nicola Sturgeon visited Brussels on Wednesday for initial talks with European Parliament President Martin Schulz and Commission President Jean-Claude Juncker aimed at protecting Scotland's place in the EU.

The EU leaders were discussing ways of addressing the growing popular dissatisfaction with the EU laid bare by the British vote, but by no means unique to the country. Populist movements in France and the Netherlands have called for referendums of their own.

Grybauskaite said she and her peers must focus on what matters for citizens, rather than political elites. That means "immigration, economic growth," she indicated.

The only way to respond to the eurosceptics and nationalists is to have "much more Europe," added Cypriot President Nicos Anastasiades. Belgian Prime Minister Charles Michel called for more joint efforts to boost security, employment and investment in the bloc.

Member states that want to integrate more quickly should "be able to do so without being hindered by those who choose to take a bit more time to advance," Michel added, a view that is opposed, however, by those fearful of being on the outer tiers of a "two-speed" Europe.

"The leaders of Europe need to ... explain to people what are the choices, what are the difficulties, what are the challenges," said Estonian Prime Minister Taavi Roivas.

According to diplomats, the leaders' statement will lay out in broad terms their objective to reform the EU without going into details. They are expected to continue discussions at another summit expected for mid-September in Slovakia.

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