European Union leaders eager for Turkey's help in the migrant crisis cautioned against promising too much to their often reluctant partner at a summit in Brussels Sunday, even as Turkey's prime minister declared the beginning of a new era for relations between the two sides.

The emergency meeting at EU headquarters centered on a plan to offer Turkey 3 billion euros ($3.2 billion), an easing of visa restrictions and fast-tracking of its EU membership process in return for which Ankara is to tighten border security and take back some migrants who don't qualify for asylum in Europe.

"I want there to be an agreement so that Turkey takes on commitments, Europe supports it, and the refugees can be welcomed," French President Francois Hollande said.

Turkey's Prime Minister Ahmet Davutoglu said he was "thankful to all European leaders for this new beginning, which is not just a beginning of a meeting but the beginning of a new process, which is very important for the future of our common bond in Europe."

According to the International Organization for Migration, almost 900,000 people fleeing conflict and poverty in the Middle East, Africa and Asia have entered Europe this year seeking sanctuary or jobs. More than 600,000 have entered through Greece, many after making the short sea crossing from Turkey.

More than 2 million refugees from Syria also live in Turkey, but according to Amnesty International, only around one in 10 are being helped by the government. The rest fend largely for themselves.

Even if support for closer relations with Turkey has often been lukewarm at best in many of the EU member states, the refugee crisis has forced a drastic revision of relations with Ankara.

"Turkey is right to expect that the EU provides relief," said German Chancellor Angela Merkel.

Others though pointed out that any aid had to be offset by Turkish commitments on reform and respect for human rights.

EU President Donald Tusk put it straight to Davutoglu during the opening session of the summit. In return for EU aid, he said, "we expect to see an immediate and substantial reduction of irregular migrants arriving to Europe." Furthermore, he added, the EU nations want Turkey "to realize the common objective of coming closer together through reforms, the upholding of the highest standards of human rights and media freedom and the implementation of agreed roadmaps and benchmarks" that are part of the EU membership talks.

Belgium's prime minister Charles Michel said Turkey could not be given a "blank check" from the EU to help it handle the roughly 2 million Syrian refugees in the country and added his nation is not ready yet to free up money. And even if Turkey has long sought to join the bloc, Michel said Turkey is "far away from membership" and "there is much progress that needs to be made."

The migrant crisis has shaken the EU to its core over the past few months when several member states proved unwilling or unable to deal with the arrival of thousands of needy people on their borders.

Tusk said the future of Europe's 26-nation passport-free Schengen travel area, a cornerstone of European unity, was in jeopardy.

"The most important one is our responsibility and duty to protect our external borders. We cannot outsource this obligation to any third country. I will repeat this again: without control on our external borders, Schengen will become history," Tusk said.

Yet in a recent membership progress report on Turkey, the EU criticized Ankara's interference with its justice system and Turkish government pressure on the media. Last week, two more opposition journalists were jailed in Turkey.

EU foreign policy chief Federica Mogherini said that there was enough to bind both sides together.

"Turkey and Europe need each other. We are facing the same problems — from the war in Syria to terrorism to the stability or instability for the region . we can be partners. We have to put all the issues we have on the table."

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Maria Cheng and Jamey Keaten contributed to this article