Nearly 600,000 migrants have reached the EU by sea so far this year, many of them travelling from Turkey.
The leaders agreed to speed up visa liberalisation talks for Turks if Turkey stems the influx and to “re-energise” talks on it joining the EU.
However, the Turkish foreign minister said the deal was still a draft and had not been agreed upon.
Feridun Sinirlioglu called the financial measures proposed by the EU “unacceptable”, according to AFP news agency.
Bulgarian Prime Minister Boyko Borisov left the Brussels talks on hearing the news.
Also on Friday, Hungary announced it was going to seal its border with Croatia at midnight (22:00 GMT) following a similar move last month to close its border with Serbia.
Hungary has been a major destination for migrants during the crisis, who often aim to continue on to Austria and Germany.
accelerate visa liberalisation for Turks wanting to visit the EU’s borderless Schengen area – if Turkey complies with certain criteria
“re-energise” 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.”
EU sources had said several countries were cautious about coming to an agreement with Turkey too quickly.
Among them were Greece, Cyprus and France.
If a deal with Turkey sticks, and if it really does help stem the flow of migrants to Europe, then this is an important moment. Those are a couple of big “ifs” though.
Turkey wants an additional €3bn in aid, but that figure has still to be agreed, and there is concern about its effect on the overall EU budget. Further concessions to Turkey – on visa-free travel to Europe, and on re-energising long-stalled EU membership talks – can best be described as preliminary.
Turkey will still have to meet certain criteria to make progress. It will also take some time to find out whether it really has either the will or the ability to stop migrants travelling to Europe.
But the very fact that the EU is paying Turkey so much attention looks like a big boost for the country’s President Tayyip Erdogan – a couple of weeks before Turkey holds another general election.
Earlier on Thursday, Mrs Merkel said all EU countries must be prepared to send security staff to the bloc’s external borders.
She said it would be unfair to ask EU countries seeing the majority of initial migrant entries to secure borders as well.
“It’s quite obvious that only a few countries today take the majority of refugees and if these countries now are asked to secure the external borders on top of that, I don’t think it would be what we could call a fair distribution of effort,” Mrs Merkel said.
She described the current situation as “very disorderly”.
In other developments:
EU foreign policy chief Federica Mogherini called for member states to address the causes of migration by providing more money for Syrian refugees in Jordan, Lebanon and Turkey and for development in Africa
Five members of a Lebanese family have drowned after a boat carrying them from Turkey to Greece capsized, relatives say. Another four are missing.
Turkey is hosting some two million migrants, most of them fleeing the war in neighbouring Syria.
Turkey has also called for the establishment of an international “safe zone” for refugees inside northern Syria – but Mr Tusk said Russia’s involvement in Syria made the idea more difficult.
Also in Brussels, UK Prime Minister David Cameron said he would present four main demands for change in the EU in November. It comes ahead of a promised referendum on the UK’s membership of the EU in 2017.