The leaders agreed to speed up visa liberalisation talks for Turks if Ankara stems the influx and to "re-energise" Turkey's accession dialogue.
Donald Tusk, the president of the European Council, said he felt "cautious optimism" over the deal.
Meanwhile a migrant thought to be Afghan was shot dead by a Bulgarian border guard after entering the country from Turkey late on Thursday.
One refugees at Turkey |
Thursday's summit in Brussels, European leaders agreed to:
. accelerate visa liberalisation for Turks wanting to visit the EU's borderless Schengen area - if Turkey complies with certain criteria
. "re-energised" talks over Turkey joining the EU.
Turkey had also asked for €3bn (£2.2bn, $3.4bn) in aid, something German Chancellor Angela Merkel said EU states were considering. Jean-Claude Juncker, the president of the European Commission, said talks over the aid would continue with Turkish officials over the coming days.
Mrs Merkel will travel to Turkey at the weekend. "There is still a huge amount to do," Mrs Merkel said. "But you cannot say that we've achieved nothing."