"I have some understanding for the fact that (Prime Minister) David Cameron wants to have some time in order to meditate," Juncker told a news conference after an EU summit.
"We want Article 50 (of the Lisbon Treaty formally stating Britain's intention to leave) to be triggered as soon as possible... It has to be speeded up. We don't have months to meditate, we have to act."
Juncker added: "What I don't understand is that those who wanted to leave (the EU) are totally unable to tell us what they want.
Juncker also said that he expected Britain to trigger Article 50 very soon after Cameron's successor is named on September 9.
"If someone from the 'Remain' camp will become British PM this has to be done in two weeks after his appointment," he said.
"If the next British PM is coming from the 'Leave' campaign it should be done the day after his appointment."
EU President Donald Tusk meanwhile said leaders appreciated that the situation needs to calm down in Britain following the Brexit vote before the next steps can be taken.
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