European Union leaders were reeling Friday after Britain's shock vote to leave plunged the EU into deep uncertainty, not least over how to negotiate the unprecedented departure of a member state.

Top EU officials tried to put on a brave face as the European enterprise — already wracked by economic woes, Greece's shaky future in the euro and Europe's inability to manage the refugee emergency — came face to face with yet another existential challenge.

As the British pound lost value and with markets jittery, EU leaders underlined that the U.K. must negotiate its exit quickly and warned that it would remain a member, with all the obligations that entails, until the talks are over. That could mean more than two years longer.

The heads of the EU's main institutions said in a statement that they want Britain to act on the vote "as soon as possible, however painful that process may be. Any delay would unnecessarily prolong uncertainty."

The statement was signed by European Council President Donald Tusk, European Commission President Jean-Claude Juncker, European Parliament President Martin Schulz and Dutch Prime Minister Mark Rutte, whose country currently holds the EU's rotating presidency.

They added that under the bloc's treaties "EU law continues to apply to the full to and in the United Kingdom until it is no longer a member."

Tusk told reporters that Britain's 27 partners were "determined to keep our unity." But, he said, "there's no way of predicting all the political consequences of this event."

He said EU leaders will meet without British Prime Minister David Cameron next week on the sidelines of a summit in Brussels "to start a wider reflection on the future of our Union."

While he admitted that the last year has been one of the toughest in EU history, Tusk said: "What doesn't kill you, makes you stronger."

Schulz announced that the European Parliament would hold an emergency session Tuesday morning, hours before a two-day summit of presidents and prime ministers, to debate the next steps.

As if Britain's departure wasn't bad enough, Cameron's resignation and decision to leave exit negotiations to his successor from October raised new worries about how long the process might drag on and possibly fuel the ambitions of others who might want to leave.

Once its intentions are officially notified, Britain would have two years to officially negotiate its departure, although London could be granted an extension if all 27 EU member states agree.

The head of the biggest bloc in the parliament fired an early warning shot, saying that Britain should expect no free ride as it negotiates its departure.

"There cannot be any special treatment for the United Kingdom. The British people have expressed their wish to leave the EU. Leave means leave. The times of cherry-picking are over," European Peoples Party leader Manfred Weber said.

He insisted that the exit negotiations "should be concluded within two years."

This insistence on a "hard exit" is aimed at discouraging other countries from wanting to leave the bloc in the belief that they might be able to negotiate a comfortable partnership from the outside.

Many European officials fear the U.K. vote will play into the hands of the far right and left and fuel calls for referendums in other countries.

The possibility to leave exists in the EU's rule book, but it's never been used before.

Whatever decisions are taken, the coming weeks and months will be frantic and uncertain, according to analysts.

"This summer will see the beginning of a tumultuous political crisis that will probably set many EU member states against one another, and will certainly reverberate around the world," warned Giles Merritt from the Friends of Europe think tank.

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