Action must be taken to prevent other countries from fleeing the EU, German Chancellor Angela Merkel has said.
Speaking at a Christian Democratic Union party executive board meeting, Ms Merkel said the financial markets are very concerned that the EU is no longer governable.
She added that all 27 remaining EU countries must consult together on the way forward following Britain's vote to leave the bloc.
However, Ms Merkel maintained that it is not the right time to pursue a quick deepening of cooperation between eurozone member states.
Instead, the EU should act on popular concerns such as securing the bloc's borders, creating jobs and improving internal security, she said.
Britain should stay in the EU to ensure it has a "seat at the bargaining table" in the future, Germany's Chancellor Angela Merkel has said.Read the full story ›
Angela Merkel has announced she is pushing "for the establishment of special security zones in Syria" to be set up near the border with Turkey so that refugees have somewhere where they can find shelter.
Speaking at a press conference today the German Chancellor said: "I have ... again demanded that we have zones where the ceasefire is particularly enforced and where a significant level of security can be guaranteed."
Merkel's comments came shortly after she visited a migrant camp on the Syrian-Turkish border where she inspected conditions and spoke to people living there.
Angela Merkel's conservatives have lost out in two out of three regional elections as Germans gave the thumbs down to her "open door" migrant policy.
The defeat was the worst case scenario for the Chancellor, who staked her legacy on her decision last year to let in over one million migrants.
Anti-immigration group Alternative for Germany (AfD) made gains after the poor showing of support for Merkel's Christian Democrats.
AfD chief Frauke Petry said: "We have fundamental problems in Germany that led to this election result."
The result is a setback for Merkel just as she is trying to use her status as Europe's most powerful leader to seal an EU deal with Turkey to stem the tide of migrants.
Addressing a rally in Baden-Wuerttemberg on Saturday, Merkel defended her decision saying: "There are situations in life - and this was the case last autumn - when you can't hold a long debate on principles.
"People are suddenly there and need protection", she added.
German Chancellor Angela Merkel has arrived in Malta for an international summit on the refugee crisis and migration to Europe.
Chancellor Merkel, who faces intense domestic pressure after offering shelter to almost a million asylum seekers this year, said the summit "would promote friendly relations with Africans", but added it would "also set out clear demands and expectations" from Europe.
African leaders have expressed concern at suggestions that Europe could sharply reduce immigration. EU officials have said that legal migration, for students and seasonal labour, could be increased in return for help cutting illegal migration.
Germany is also facing an influx of people from Syria, and has warned that it could start sending Syrian refugees back to other EU states. In response, Hungary said it would not take any and Slovenia began to put up new border fences.
Germany wants to help Britain with its proposals to reform the European Union and is confident a solution can be found, Angela Merkel has said.
The German chancellor confirmed she had spoken to David Cameron about his proposals by phone on Monday.
"I know of the demands, so what is on the table now is no surprise," she said at a press conference alongside South African President Jacob Zuma.
"We want to take a solution-orientated approach to dealing with these proposals."
"There are some difficult points, and some less difficult points.
"But if one has a spirit of wanting to solve this then I have a certain confidence that this can work out."
Many Greeks have reacted angrily to news of the deal agreed by eurozone leaders, with many directing their anger at the German Chancellor Angela Merkel and especially towards finance minister Wolfgang Schaeuble.
Newspapers laced the morning's headlines with references to World War Two and railed against what they see as Berlin's attempts to humiliate Greece.
In particular, Greeks bristled at Schaeuble's proposal, which was not included in the final deal, for a temporary Greek exit from the euro zone, which many saw as tantamount to expulsion by stealth.
A poster depicting a defaced image of Schaeuble on the wall of a Eurobank branch in Athens highlighted the anger felt by some on the streets of Greece.
Greece has received a "generous offer" for a bailout, according to the German chancellor, in a speech.
She also said that if the Greek government wants more talks after this weekend's referendum, she will not say no.
David Cameron is to round off his whirlwind tour of major European leaders with a crucial meeting with German Chancellor Angela Merkel.
The Prime Minister is looking to build support for his plans to renegotiate the terms of the UK's membership of the EU, and he'll need the agreement of the German premier if he is to have any hope of success.
However, there has been little sign of enthusiasm for treaty change. France and Germany have reportedly agreed that closer integration of the eurozone countries can be achieved without altering treaties - potentially reducing Britain's leverage.
This morning Mr Cameron will be in Warsaw for talks with Polish counterpart Ewa Kopacz, before heading for Berlin to see Mrs Merkel.