The European Union offered Turkey a possible 3 billion euros in aid and the prospect of easier travel visas and "re-energised" talks on joining the bloc in return for its help stemming the flow of migrants to Europe.
Though the plan put no figure on "substantial and concrete new funds" the EU would offer, German Chancellor Angela Merkel said the figure of 3 billion euros, which EU officials said Ankara had requested, had been discussed and seem reasonable.
In formal conclusions agreed by the 28 national leaders at a meeting that ended after midnight, Turkey was offered an accelerated path to giving its citizens visa-free travel to the EU, provided it met previously agreed conditions.
"The accession process needs to be re-energised with a view to achieving progress in the negotiations in accordance with the negotiating framework and the relevant Council conclusions," they said, in language couched cautiously to reflect concerns in Cyprus and other states about easing off pressure on Ankara.