The German and French leaders are in "full agreement" on dealing with the "Brexit," according to the French presidency. But elsewhere, uncertainty about what happens next seems to prevail.
Ahead of an EU-wide summit on Tuesday and Wednesday, German Chancellor Angela Merkel and French President Francois Hollande have said they are in "full agreement on how to handle the situation" after British citizens voted last Thursday to leave the bloc, French presidency sources say.
A source close to Hollande told the AFP news agency that both leaders had agreed in a phone call on the need for "the greatest clarity to avoid any uncertainty," and had called for the quick European action "on concrete priorities."
However, the clarity and certainty they are calling for currently seem like impossible goals, as the European Union, and Britain itself, struggle to come to terms with the UK's decision to become the first member state ever to quit the bloc.
Calls for swift British action
Germany's EU Commissioner Günther Oettinger on Monday joined the chorus of voices calling on Britain to clarify its intentions after the Brexit vote, telling broadcaster Deutschlandfunk that the Conservative Party under Prime Minister David Cameron must swiftly decide on what course to take.
"With every day of uncertainty, investors in the whole world will be discouraged from investing in Great Britain or from believing in Europe," Oettinger said.
His comments echoed those made at the weekend by the president of the European Parliament, Oettinger's compatriot Martin Schulz.
Schulz called for Britain to apply to leave on Tuesday at the EU summit to make it easier for the bloc to get back on its feet quickly after the shock of losing one of its most powerful economies.
On Monday, Merkel's spokesman Steffen Seibert also said that the chancellor rejected any long delay in Britain's departure from the bloc.
"The German government does not want an impasse. That cannot be in anyone's interest in Europe," Seibert said in Berlin.
He added that Merkel was also opposed to "informal exit talks" with Britain before it officially applied to leave the EU.
Wait and see?
However, Britain's Cameron has so far refused to invoke Article 50 of the EU's Lisbon Treaty and has signalled that he wants to wait several months before beginning the country's exit from the bloc, leaving his European partners in a state of limbo. Invoking Article 50 would trigger some two years of exit negotiations.
Cameron, who supported the "Remain" campaign at Thursday's referendum, is expected to stay on in a caretaker role until his Conservative Party chooses a new leader. By Cameron's timetable, a replacement should be found ready for the Tories' party conference in October, a delay that might not prove palatable on the continent.
Even those British politicians behind the "Leave" campaign seem to be in considerable doubt as to how to proceed without damaging British interests.
Boris Johnson, who is favorite to become the next Conservative prime minister, has tried to allay fears about the country's economic future by claiming that it would continue to have acess to the EU single market.
What he could not explain, however, was how Britain can continue to partake in free trade in Europe without accepting precisely the EU regulations that those in the "Leave" campaign want to jettison, including rules on freedom of movement for EU citizens.
The fallout from the referendum result has also wreaked havoc within the opposition Labour Party, with senior parliamentarians withrawing their backing for leader Jeremy Corbyn, who has faced widespread accusations of failing to galvanize Labour supporters into voting against the "Brexit."
Historic decision
On mainland Europe, Merkel and Hollande will be meeting on Monday with Italian leader Matteo Renzi in Berlin to discuss the consequences of a British EU exit for the bloc.
Then, on Tuesday, leaders from all 28 EU member states, including Cameron, will meet in Brussels for a two-day summit to hammer out a plan for how to proceed in the unprecedented situation.
The United Kingdom joined the forerunner of the EU, the European Economic Community, 43 years ago. Many fear that its decision now to leave the bloc could fuel euroskepticism in other member states as well, thus undermining a project that is widely seen as promoting not only economic prosperity, but also peace and international harmony.