The Europeans, none more so than German Chancellor Angela Merkel, are under pressure to manage the biggest influx of people since World War Two, the bulk of them to Germany. The crisis has helped populist opponents and set nations against each other, straining the open internal borders of the EU.
Before the summit itself, Merkel met leaders of some other EU states which have taken in many refugees -- Sweden, Finland, Austria and the Benelux countries -- and said afterwards they had discussed how they might resettle more of them directly from Syria rather than wait for families to reach the EU via dangerous smuggling routes across the Mediterranean.
She said they had discussed no figures. German media reports had spoken earlier of up to 400,000 Syrians being resettled.
Measures the EU has taken have done little to control migrant movements. While winter weather may lower the numbers for a few months, it is also worsening the plight of tens of thousands stuck by closing borders in the Balkans.
Sunday's summit, called just days ago as Brussels tried to clinch a deal offered over a month ago, has been complicated by Turkey's downing of a Russian warplane on the Syrian border.
That has complicated European efforts to re-engage with Moscow, despite a continued frost over Ukraine, in order to try to advance a peace in Syria that could end the flight of refugees and contain Islamic State. Davutoglu will remain in Brussels for a meeting with fellow ministers from NATO.
Irish Prime Minister Enda Kenny said tensions between Ankara and Moscow over the downing of the warplane were of "enormous concern." The EU's foreign policy chief Federica Mogherini said the incident should not affect the prospect of finding a political deal on Syria.