Turkey demanded on Thursday that the European Union start easing restrictions on Turks travelling to the EU next year if it wants cooperation to stem the flow of Syrian refugees and other migrants to Europe.

As EU leaders met in Brussels to discuss making concessions to Turkey in return for help with Europe's migration crisis, EU sources said Turkish ministers asked EU negotiators in Ankara for 3 billion euros ($3.41 billion) in financial aid and a broadening of long-running talks on eventual Turkish membership of the bloc.

Turkey was also seeking more high-level political dialogue with invitations for President Tayyip Erdogan to summits after an ice-breaking visit he made to Brussels earlier this month.

EU diplomats said an existing plan to ease visa requirements for Turks could be speeded up, but only if Ankara met the technical conditions, and that member states were prepared to discuss further funding, although on a more modest scale.

Requests for Turkey to be put on a list of "safe countries", whose nationals would not normally be granted asylum in Europe, broader accession talks and more EU-Turkey summits could find support, they said.

Turkey and delegates from the European Commission in Ankara were "close to finalising" agreement on a joint action plan they hope will improve conditions for the more than 2 million Syrians in Turkey to encourage them to stay, EU officials said.

The plan also envisages cooperation on border patrols and fighting people-smugglers.

"It's a reset of our relationship, together with a firm commitment on both sides to cooperate on dealing with the refugee issue," a senior EU official told Reuters.

Turkish Prime Minister Ahmet Davutoglu said Ankara would not finalise a previously drafted agreement to take back migrants rejected by the EU without progress on the visa issue.

"We will not sign the readmission agreement before steps are taken on the Schengen visa and thus a visa liberalisation is secured for Turkish citizens," he told a television interviewer, saying he wanted a deal by the first half of next year.

Parallel, linked agreements on readmission and visa-free travel were made in late 2013, laying out conditions to be met, and expectations, that would take some three to four years.

"CONDITIONS APPLY"

French President Francois Hollande said of the Turkish demand: "Just because we want Turkey to help us by keeping back refugees, we mustn't ease restrictions unconditionally ... So there will be a proposal that will set many conditions."

Chancellor Angela Merkel told the German parliament before leaving for the summit that Europe needed to offer better support to help Turkey deal with the influx of refugees from war-torn neighbours. Over two million Syrians are in Turkey.

"Without a doubt Turkey plays a key role," said Merkel, who will visit Istanbul on Sunday. "Most war refugees that come to Europe travel via Turkey. We won't be able to order and stem the refugee movement without working together with Turkey."

Merkel's trip to meet Erdogan just weeks before the second Turkish general election this year is a key political gesture. In a smaller concession, the European Commission has postponed its annual progress report on Turkey's accession bid, often highly of human rights.

Yet embracing Turkey and especially Erdogan, who critics see as increasingly authoritarian, poses dilemmas for EU leaders. Many accuse the president of weakening civil rights in the last couple of years, notably regarding minority Kurds and the media.

But the EU's political priority has changed.

"In our neighbourhood, we are not asking any more for fundamental rights after the Arab Spring," said a senior EU political leader. "We are asking for stability."

Many, notably in Berlin and Paris, doubt whether such a populous, poorer and mostly Muslim country can ever join the Union. Yet the EU is desperate for Turkey's help and ready to meet some of Erdogan's demands, notably for easier travel for Turks to the EU, economic cooperation and diplomatic goodwill.

Efforts to end the division of Cyprus between the Greek-speaking state that is an EU member and the Turkish-backed one in the north of the eastern Mediterranean island are also a factor in relations. EU diplomats worry that Erdogan may use the migration crisis as added leverage.

"We understand the added value of Turkey," one said. "But we cannot give it carte blanche."

"GUARANTEES"

Adding to uncertainties in negotiating any deal with Turkey is the turmoil that followed a bombing Ankara blames on either Kurds or Syria-based Islamists, as well as a snap parliamentary election on Nov. 1 that will determine Erdogan's future powers.

European Council President Donald Tusk said before chairing the summit: "We need ... guarantees that Turkey's response to our offer will be as substantive as ours."

Pouring cold water on Turkish calls for Europe to support its proposals for "safe zones" for refugees in northern Syria, Tusk said he wanted to focus on "more realistic targets". He noted that Russia's recent military intervention in Syria complicated matters, given Moscow's opposition to safe zones.

The EU is offering Turkey additional funding to help build facilities for the large numbers of Syrians it has taken in. It is also considering easing visa conditions for Turks, at first for business travel and possibly students -- though this is bound up with legal benchmarks in the EU accession process.

Diplomats say the visa issue is important for Ankara, as is a general willingness to lend Erdogan international prestige.

Draft conclusions of the summit, seen by Reuters, read:

"Successful implementation will contribute to accelerating the fulfilment of the visa liberalisation roadmap. The EU and its member states stand ready to increase cooperation with Turkey within the established framework and step up their political and financial engagement substantially."