Brexit - European Union leaders have insisted that the UK must move swiftly to negotiate leaving the organisation, saying any delay would prolong uncertainty.
European Commission head Jean-Claude Juncker stressed the "Union of the remaining 27 members will continue".
The UK voted by 52 percent to 48 percent to leave the EU yesterday, and David Cameron has announced he will step down as PM by October.
He has said it will be up to the new PM to invoke the article that will begin the UK's withdrawal.
Global stock markets fell heavily on the news of the so-called "Brexit". The value of the pound has also fallen dramatically.
A meeting of 27 EU leaders has been scheduled for Wednesday to discuss Brexit - but Mr Cameron is not invited.
Mr Juncker held crisis talks with European Parliament President Martin Schulz, president of the European Council Donald Tusk and Dutch PM Mark Rutte on Friday morning.
They then released a statement saying they regretted but respected the British decision.
They called for the UK "to give effect to this decision of the British people as soon as possible, however painful that process may be. Any delay would unnecessarily prolong uncertainty".
They added that the deal agreed with Mr Cameron in February to protect London's financial markets, curb immigration and opt out of closer union "ceases to exist" and "there will be no renegotiation".
Later, Mr Schulz criticised the decision by Mr Cameron and his divided Conservative party to hold the vote.
"The European Union as a whole was taken as a hostage by a party internal fight of the Tories," he said.
"And I'm not satisfied today to listen that he wants to step down only in October and once more everything is put on hold until the Tories have decided about the next prime minister."
The UK must now invoke Article 50 of the Lisbon Treaty to leave, which then allows for two years for withdrawal to be negotiated.
German Chancellor Angela Merkel expressed "great regret" at the British decision, saying: "This is a blow to Europe and to the European unification process". She said she would meet Mr Tusk, French President Francois Hollande and Italian PM Matteo Renzi in Berlin on Monday
Mr Hollande said the vote "seriously puts Europe to the test", adding: "I respect this painful choice. France will continue to work with this friendly country"
Russian President Vladimir Putin said the decision showed the UK's unhappiness with migration and security.