The German Chancellor, Angela Merkel, has said there can be no talks on Brexit before the UK formally begins the process of leaving the EU.
While accepting the UK needed time, she added it should not be a "long time".
Mrs Merkel is due to meet French and Italian leaders later in Berlin, with the speed of negotiations for the UK's exit high on the agenda.
UK Prime Minister David Cameron has confirmed the UK is not ready to begin the formal withdrawal process.
Billions more dollars were wiped off the value of shares in Europe and on Wall Street as a result of market uncertainty on Monday. London's benchmark share index was down 2.75% while Germany's leading index fell by 3%.
Last Thursday, the UK voted 52-48 in favour of leaving the EU in a historic referendum, throwing the economy and politics into turmoil.
US Secretary of State John Kerry has said his country's "special relationship" with the UK will be maintained. "The vote did not come out the way US President [Barack] Obama and I had expected but that's democracy," he told reporters in Brussels.
What exactly did Mrs Merkel say?
"The reality is that a majority of British citizens voted to leave... so I await a communication about Article 50 [the formal trigger for withdrawal] from the UK addressed to the EU," Mrs Merkel said.
"We should not wait a long time. I do understand that the UK will consider things for a while. There cannot be any informal negotiations until we get that message from the UK.
"We can't have a permanent impasse," she was quoted as saying by Reuters news agency.
Once the UK invokes it, Article 50 of the Treaty of Lisbon sets out a two-year timetable to reach an exit deal. But UK PM David Cameron, who will step down by October, says he will leave the timing to his successor. He is due to make a special address to parliament later.
The Leave campaign says there is no need to rush the UK's exit.
France and Germany have insisted they are in "full agreement" on Brexit, although French Finance Minister Michel Sapin said on Monday this meant Britain should "go quickly".
How is the UK government responding?
Mr Cameron took to the floor of the House of Commons to say he had spoken to European leaders and told them "the British government [would] not be triggering Article 50 at this stage".
"Before we do that we need to determine the kind of relationship we want with the EU," he said.
He repeated his promise to stand down as prime minister this year and said it would be up to his successor to invoke Article 50.
The chancellor, who backed Remain, tried to reassure financial markets that the UK was in a strong position to tackle the inevitable volatility.
Despite suggesting before the vote that an emergency budget would be needed, he indicated that this would not now be an immediate priority, preferring to leave any adjustments to the economy to the new PM.
He appeared to rule out resigning in the near future.
What are the Leave campaigners saying?
Boris Johnson, the leading light of the Leave campaign, used an article in the Daily Telegraph to try to soothe British fears.
"EU citizens living in this country will have their rights fully protected, and the same goes for British citizens living in the EU. British people will still be able to go and work in the EU; to live; to travel; to study; to buy homes and settle down," he said.
He also suggested the UK would still have access to the EU's single market, a remark quickly challenged by the German Business Institute and Merkel ally Michael Fuchs, MP.
Mr Fuchs said: "It will be possible, of course, but not for free - you have to see with Norway, with Switzerland, you have to pay a certain fee. And the per capita fee of Norway is exactly the same as what Britain is now paying into the EU. So there won't be any savings."
What's the latest political fallout in the UK?
Labour faced more turmoil, with further resignations of shadow ministers on Monday. Twenty-three of the 31 members of the shadow cabinet have now gone.
Mr Corbyn has announced a new team but faces a possible no-confidence vote.
Nicola Sturgeon, the first minister of Scotland, which voted 62% for Remain, told the BBC the Scottish parliament could try to block the UK's exit from the EU.
She also confirmed a second Scottish independence referendum was back on the table.
Brexit: A busy week ahead
Monday: Angela Merkel holds crisis talks in Berlin, first with EU President Donald Tusk, then with Mr Hollande and Mr Renzi (statement to media expected at 18:30 local time, 16:30 GMT).
Tuesday: Extraordinary European Parliament session in Brussels on Brexit vote 10:00-12:00 (08:00-10:00 GMT), including speeches by Mr Tusk, European Commission President Jean-Claude Juncker and party leaders, probably including UKIP's Nigel Farage. There is also an EU summit (European Council) in Brussels, at which David Cameron will brief the other EU leaders over dinner, from 19:45 (17:45 GMT), explaining the political fallout in the UK
Wednesday: Second day of EU summit will feature breakfast talks between 27 leaders - Mr Cameron not attending. Talks focus on UK's "divorce process" as stipulated by Article 50, and Mr Tusk will "launch a wider reflection on the future of the EU"; press conferences in afternoon.