The UK faced calls from other European Union nations for a quicker start to the process of seceding from the EU, deepening the bloc's frustration with British Prime Minister David Cameron.
Cameron said he would resign and let a successor who may be chosen by a Conservative Party conference in October trigger the negotiations on the UK's exit from the EU. Most EU ministers who met in Luxembourg to discuss the process argued that "we should start this as soon as possible," said Bert Koenders of the Netherlands.
"You are in or you're out -you can't have your cake and eat it," Koenders, the Dutch foreign minister, told reporters. "That means that, at the moment that there is an outcome, it's important that the insecurity for citizens in Europe is as short as possible and that there is clarity on this."
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Koenders, who chaired the Luxembourg meeting because the Netherlands holds the EU's six-month rotating presidency, said the bloc is seeking "transparent and predictable" discussions with the UK on its departure and wants to avoid a lengthy "vacuum." Meanwhile, other ministers expressed concerns about the British referendum result stoking centrifugal forces in the EU.
"What I am afraid of is that those parties that are xenophobic, nationalistic, protectionist get a positive feedback from this Brexit outcome," said Ann Linde, Sweden's minister for European affairs. "The situation we are in now is a bad situation."
Belgian Foreign Minister Didier Reynders signalled the UK is in more political trouble than the EU, calling the UK referendum result a "dangerous choice" for the country.
"It will have to engage in a negotiation with the European Union to leave the union," Reynders said. "There is also a risk of the disunion of the United Kingdom."
Back in the EU capital Brussels, Gianni Pittella, who leads the Socialist group in the European Parliament, captured continental frustration over Cameron's tenure as British prime minister by saying that the UK referendum was a "crazy idea" prompted by internal party considerations.
Over one million sign petition calling for second Brexit vote
An online petition for a second referendum on the UK's membership of the European Union was signed by almost 1.2 million people by Saturday morning.
The online petition, set up after Britain's shock decision to sever itself from the EU, says "We the undersigned call upon HM Government to implement a rule that if the remain or leave vote is less than 60% based a turnout less than 75% there should be another referendum."
UK voters backed Brexit by 51.9 per cent to 48.1 per cent with a turnout of 72.2 per cent, the Electoral Commission said. The move, asking for a rule change on a vote that has already taken place, could trigger a lawmaker debate. Any petition exceeding 100,000 signatures is eligible for debate; Parliament's Petitions Committee makes the final decision on whether to hold one.
Parliament debated whether to ban Donald Trump from the UK in January because of his comments about preventing Muslims from entering the US after 587,000 people signed a petition. It didn't work: Trump visited Scotland Friday.