On the eve of the key gathering, outgoing UK Prime Minister David Cameron again said he will not trigger the Article 50 exit procedure, the starting gun for Britain's withdrawal from the EU.
On Tuesday, the embattled Cameron said, "I'll be explaining that Britain will be leaving the EU but I want that process to be as constructive as possible, and I hope the outcome can be as constructive as possible, because of course, while we're leaving the EU we mustn't be turning our backs on Europe.
"These countries are our neighbours, our friends, our allies, our partners and I very much hope we'll seek the closest possible relationship in terms of trade and cooperation and security, because that is good for us and that is good for them. And that's the spirit in which the discussions I think will be held today."
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The vote to leave the EU will dominate the two-day summit, which is due to conclude on Wednesday.
Cameron's desire to delay triggering Article 50 found an ally in Dutch Prime Minister Mark Rutte, whose country currently holds the rotating EU Council presidency and who warned that it would be "unwise" to push the UK into triggering Article 50.
Despite this, there is a growing clamour for negotiations to start as soon as possible, with the Belgian Prime Minister Charles Michel demanding "more clarity from Cameron on the Brexit timetable."
Speaking after a meeting with French President François Hollande and Italian Prime Minister Matteo Renzi in Berlin on Monday, German Chancellor Angela Merkel was more conciliatory, saying, "We are in agreement that Article 50 of the European treaties is very clear.
"A member state that wishes to leave the EU has to notify the European Council [of its decision]. There can't be any further steps until that has happened. Only then will the European Council issue guidelines under which an exit will be negotiated."
She went on, "That means that, and we agree on this point, there will be neither informal nor formal talks on a British exit until the European Council has received the [UK's] request for an exit from the EU."
On Tuesday, Merkel also told the Bundestag that the UK cannot "cherry-pick" the terms of its new relationship with the EU after Brexit, stressing that the EU's 'four freedoms' - free movement of goods, services, people and capital - cannot be split up.
Further eve-of-summit comment came from European Council President Donald Tusk, who said, "I want to say that while respecting the will of the UK voters, we also have to respect our treaties; and, according to them, it is the British government who initiates the process of exit from the EU.
"And this is the only legal way we have. Everyone should be aware of this fact, which means that we also have to be patient if there is such a need.
"Europe is ready to start the divorce process, even today, without any enthusiasm, as you can imagine. This is not the scenario we were dreaming about. We have precise procedures, we have a ready work plan.
"But I would like to underline very clearly: without the notification from the UK, we will not start any negotiations on divorce process or on our future relations."
Tusk, a former Polish Prime Minister, said that the day after Brexit he felt "as if someone very close to me left our home and in the same second I felt also how dear and precious this home was to me."
He added, "Brexit is not only about procedures, politics and interests, it is also about our emotions and feelings and I am absolutely sure that I am not alone with this kind of feelings but what has happened, happened and we have to move on also with our regular agenda."