EU leaders are holding a key summit with Turkey on how to deal with Europe's worst refugee crisis since World War Two.
The EU is pressing Turkey, through which many migrants transit, to take some back in return for $3.3bn in aid.
The Brussels talks have been extended into a working dinner between the 28 EU leaders and Turkey's prime minister.
Meanwhile a rift has emerged among EU powers on the closure of the main route through the Balkans.
A draft communique had revealed the EU was about to declare the route "now closed", but the German government rejected this as "speculation".
Last year, more than a million people entered the EU illegally by boat, mainly going from Turkey to Greece.
Many migrants leave Greece in an attempt to reach northern Europe, but eight countries have introduced temporary border controls.
Some 13,000 migrants are currently stranded in northern Greece, after Macedonia, backed by Croatia, Hungary and Slovenia, closed its border to all but a trickle of migrants.
The human cost of the migrant crisis was brought home again on Sunday when a boat capsized off Turkey with the loss of 25 lives.
The summit was initially due to be in two parts - the first session from 12:00 GMT involving Turkey, while in the afternoon EU leaders will seek to reach a common approach to the crisis.
After the talks started, however, the EU announced that a working dinner would be added to discuss "new ideas" on the crisis offered by Turkish Prime Minister Ahmet Davutoglu.
Ahead of the talks, Mr Davutoglu said Turkey was "indispensable" for the EU, just as Europe was for Turkey.
German Chancellor Angela Merkel said she anticipated a "difficult discussion".
A draft summit communique reported by journalists on Sunday had declared that "irregular flows of migrants along the Western Balkans are coming to an end; this route is closed".
But Mrs Merkel said: "Today is about finding a lasting solution together with Turkey... trying to find a way to stop illegal migration and improving the living conditions for the refugees."
A German government source told the BBC there was no point saying the route was closed when 300-500 people still arrived in Germany everyday this way.
UK PM David Cameron said there was "no prospect of Britain joining a common asylum process in Europe".
"We have an absolutely rock-solid opt-out from these things," he said.
The EU wants Turkey to take back thousands of migrants who do not qualify for asylum. In return the EU will discuss plans to resettle in Europe some refugees already in Turkey.
EU leaders are also likely to raise the issue of the Zaman newspaper. On Friday, a Turkish court ordered the seizure of the opposition journal, increasing fears for media freedom. Two days later it was publishing pro-government articles.
The EU said last October it would relocate 160,000 asylum seekers, mainly from Greece and Italy, but there was strong opposition among some members and fewer than 700 migrants have moved.
The EU may now overhaul its Dublin Regulation, which requires asylum seekers to lodge claims in their EU country of arrival, and instead adopt a centralised system for processing applications.
The future of the Schengen agreement - which allows passport-free travel in a 26-nation zone - will also be on the agenda. Eight members have introduced temporary border controls, and EU leaders will be anxious to save a system thought to bring billions of euros to Europe's economy every year.
'All we do is sleep'
More than 2,000 migrants, mostly from Syria, Iraq and Afghanistan, continue to arrive daily in Greece from Turkey.
The Idomeni crossing on the Greece-Macedonia border has become the latest focus of the migrant crisis.
One camp resident, Syrian refugee Narjes al Shalaby, told the Associated Press news agency: "All we do here is sleep, wake up, sleep," she said. "We get hungry, we wait in the queue for two hours for a sandwich, we come back, we sleep some more."
Separately, Nato says it is expanding its naval mission against people-smuggling in the Aegean Sea to cover Turkish and Greek territorial waters.
EU Commission spokesperson for migration Natasha Bertaud told the BBC all migrants rescued in Greek waters would be taken to a Greek island and screened.
All economic migrants would then be returned to Turkey to be screened again and "if they have no right to international protection" sent back to their country of origin.
All migrants rescued by Nato in Turkish waters would be taken back to Turkey, which would decide if they were economic migrants.
The UK has announced that the amphibious landing ship RFA Mounts Bay will join naval vessels from Germany, Canada, Turkey and Greece in the area.