ISTANBUL/BERLIN (Reuters) - German Chancellor Angela Merkel offered Turkey the prospect of support for faster progress on its bid to join the European Union on Sunday in return for cooperation in stemming the flow of migrants and taking back those rejected by Europe.

Speaking in Istanbul at a joint news conference with Turkish Prime Minister Ahmet Davutoglu, Merkel said Germany could help accelerate the path to visa-free travel to the EU for Turks and push forward Ankara's protracted EU membership talks.

In return, she expected Turkey to agree more quickly to take in migrants sent back by the EU, so-called "readmission agreements" that Davutoglu has said he will sign up to only if there is progress on liberalizing the visa regime for Turks.

"I think we have used the crisis we are experiencing, through a very disorderly and uncontrolled movement of refugees, to again achieve closer cooperation on many issues, both between the European Union and Turkey, and between Germany and Turkey," Merkel said after meeting the Turkish premier.

Merkel, who only 10 days ago reiterated her opposition to Turkey joining the EU, said the talks were "very promising". Faster Turkish accession may be hard for some in her conservative party, long opposed to Turkish membership, to swallow.

Dubbed a "punch-bag" for her own party by some German media due to frustrations over the refugee crisis, Merkel wants to cement a European deal with Turkey on aid and closer ties in return for help in encouraging refugees there to stay put.

She has resisted pressure to tighten Germany's border controls and turn away refugees arriving from Austria, even as Germany expects 800,000 to 1 million new arrivals this year.

Both the Turkish and German leaders said they had agreed there could be no lasting solution to the migration crisis without resolving the conflict in Syria, from where more than 2 million refugees have now fled to Turkey.

A "safe zone" in northern Syria, a proposal long championed by Turkey but which has gained little international traction, is badly needed, Davutoglu said.

"Our priority is to prevent illegal immigration and reduce the number of people crossing our borders. In that respect we have had very fruitful discussions with the EU recently," he said.

But Davutoglu said while progress had been made on an EU offer to Turkey last week of an action plan including "re-energized" talks on joining the bloc, several issues remained to be resolved.

"Firstly, the sharing of the refugee burden should be fair. The amount of aid ... is secondary. What is more important is the common will to tackle this issue. Turkey has been left alone in recent years," he said.

Visa-free travel for Turks should be brought forward to July 2016 instead of the current planned 2017 in exchange for Turkey signing up to the readmission agreement, he said. He also said Turkey should have a seat at EU summits.

"Germany is ready to offer support," Merkel said. "If we take the question of visa liberalization, we can talk in the German-Turkish working group ... about specific possibilities to push through visa facilitation."

Mutual Benefits

Just two months ago, Merkel was practically able to dictate terms to Greece over an aid plan to tackle its debt crisis. Over neighboring Turkey she has far less leverage.

President Tayyip Erdogan, whom Merkel also met, said he had asked her - as well as France, Britain and Spain - for support on accelerating Turkey's EU membership bid.

Erdogan discussed with Merkel the opening of five so-called chapters of the accession process, concerning harmonizing rules on energy, economic policy, fundamental rights, justice and security policy.

Merkel said Germany was ready to open the chapter on economic and monetary policy this year, and make preparations for opening the chapters on rights and justice.

Erdogan and his ruling AK Party, which faces a general election on Nov. 1, have an interest in avoiding any suggestion of a sellout to help ungrateful Europeans. He has used the opportunity to grandstand, on Friday accusing the EU of insincerity in talks on Turkish membership.

In truth, both Erdogan and Merkel know there is no near-term prospect of Turkey joining the EU. But both can still gain something from Sunday's meeting.

For Merkel, nailing down Turkey's commitment to the action plan is important to stemming the refugee flow and relieving the political pressure on her at home.

For Erdogan and the AKP, winning the promise of an accelerated path to visa-free travel to the EU for Turks could be an election boon.