European Union leaders have hailed a potential breakthrough in talks with Turkey aimed at stemming the flow of migrants streaming into the continent.
Negotiations in Brussels broke up after more than 12 hours of discussions without a final agreement.
But leaders said a Turkish proposal to return all migrants who make it across the Aegean to Greece could provide the basis of a settlement that would finally close the refugee trail through the Balkans.
In return for taking back the refugees, Turkish prime minister Ahmet Davutoglu wants the EU to resettle an equal number of Syrian refugees direct from his country - although Britain would not be affected as it is outside the Schengen area.
He also called for a doubling of EU aid - to more than £4 billion - to support the more than 2.5 million refugees in Turkey as well as faster progress on easing visa restrictions on Turkish nationals and talks on Turkey's application for EU membership.
Prime Minister David Cameron said: "It has been a long and difficult evening but I think we do have the basis for a breakthrough which is the possibility that in future, all migrants who arrive in Greece will be returned to Turkey.
"That would, if implemented, break the business model of the people smugglers and end the link between getting in a boat and getting settlement in Europe.
"That is something that I have been arguing for for a year and I think this is significant, but only if it is fully implemented and that's what needs to happen next."
European Council president Donald Tusk described the talks as the "most promising moment" in the effort to find a way of deterring migrants - many fleeing the conflict in Syria - making the perilous sea crossing to Europe.
"All of us are aware that in fact we have a breakthrough now. The new proposal of our Turkish friend is a real chance to make progress in all aspects of our joint venture," he said.
EU leaders will resume discussions on the proposals when they meet again in the Belgian capital for further summit talks later this month.
Mr Davutoglu - who brought a more ambitious than expected set of proposals to the meeting - stressed that they had to be treated as a "package" if there was to be a deal.
"This is a humanitarian process helping refugees but at the same time it is a strategic issue for us that Turkey will be admitted to the EU," he said.
There was widespread agreement that more money would need to be found to help the Turks cope with the more than 2.5 million migrants currently in the country.
German chancellor Angela Merkel said: "A further three billion euros (£2.3 billion) will be needed at the request of Turkey. We said in principle that this was a welcome approach."
British sources also indicated support for additional funding - provided the new arrangements were shown to be working..
"If that system is working, we will look at that. We will not turn the tap off," one source said.