Turkey said Monday that it would do more than the European Union has asked of it to curb the flow of migrants across the Aegean Sea, but only in return for billions of dollars in aid and a new hearing on Turkish membership in the 28-nation group.

The proposal, which came at the beginning of a bargaining session in Brussels, caught E.U. negotiators by surprise, and what had been planned as a one-day session was prolonged.

The E.U. had hoped to pressure the government in Ankara into accepting a plan under which non-Syrian migrants who had reached Europe would be sent back to Turkey. The Turks clearly saw this as an opportunity to exert some leverage in response.

The E.U. plan comes amid a worrisome backdrop: Thousands of desperate refugees and others are stranded in makeshift camps in Greece because Macedonia has barricaded its border, and the human tide into Europe is likely to grow as the weather warms.

But Turkey — the main pathway for asylum seekers, economic migrants and others in the past year — has set a high bar for agreeing to the plan.

At stake is billions of dollars in aid and revived talks over Turkey’s decades-long push to join the E.U., where opponents of Turkish membership have cited many potential obstacles including crackdowns on free expression and dissent.

The deal, originally proposed in November, reflects an increasing desire across Europe to curb the flow that brought more than 1 million migrants to the continent last year — even if it means resettling them in a place many view as unsafe for asylum.

According to Human Rights Watch, Turkey does not provide adequate protection for refugees and has frequently sent asylum seekers back to Syria. Although it has ratified the 1951 Refugee Convention, Turkey is the only country in the world that recognizes refugee status only for citizens of certain countries. Among those in the current migration, only Syrians can claim such status.

In what seemed like a test for European leaders, the Turkish government on Friday seized control of Zaman, the country’s largest newspaper. Although the E.U. considers media freedoms a fundamental right, European leaders may look the other way if Ankara agrees to help on migrants.

In Brussels on Monday, French President François Hollande insisted that Europe’s reliance on Turkey’s participation did not mean that the E.U. condoned restrictions on the news media. “Cooperating with Turkey doesn’t mean we should not be extremely vigilant about press freedom,” Hollande said. “And I am.”

Prime Minister Ahmet Davut­oglu surprised delegates in Brussels with Turkey’s expanded proposal. In addition to taking back non-Syrian migrants denied asylum in Europe, Turkey also promised to take migrants intercepted in its territorial waters. And it pledged to crack down harder on smuggling groups.

In return, diplomats said, it requested far more aid money, expedited visa-free travel for Turkish citizens in Europe, and accelerated deliberations on its accession to the bloc.

“We are not here just to talk about the migrants,” Osman Sert, Davutoglu’s spokesman, said Monday. “Turkey’s accession to the E.U. is an issue for us here.”

E.U. diplomats seemed willing to compromise on existing visa restrictions, provided that Turkey change its visa policies for Islamic states and introduce biometric passports.

By Monday afternoon, Turkey and the E.U. had tentatively agreed to 3 billion euros ($3.3 billion) in addition to the 3 billion euros Europe had initially promised in aid for Syrian refugees in Turkey. But discussions continued late into the night.

Speaking from Turkey on Monday, President Recep Tayyip Erdogan complained that although four months have passed since the E.U. promised aid, no money has been received.

“My prime minister is currently in Brussels,” Erdogan said. “I hope he will return with the money.”

More than 1 million migrants reached Europe by sea last year, and about 2,000 people are arriving in Greece from Turkey every day. On Sunday, local media reported, at least 25 people drowned off the Turkish coast attempting to reach Greece.

Still grappling with a staggering debt crisis, Greece has neither the resources nor the infrastructure to shelter the constant stream of migrants.

National differences on migrant policies were clear throughout the deliberations in Brussels. German Chancellor Angela Merkel, for instance, was firm in her opposition to permanent border controls; Austrian Chancellor Werner Faymann argued the opposite. “It has been too easy for many to simply wave through the refugees,” he said. “The more clearly we argue against this, the better.”

European leaders worry that E.U. criticism of Turkish policies might jeopardize the deal, but refugee advocacy groups, such as the U.N. Refugee Agency and Amnesty International, have criticized Turkish actions toward migrants.

Nothing in Turkish law prohibits officials from placing those who have fled other conflict zones — such as Iraq and Afghanistan — in detention camps or even from deporting them altogether.

Read more:

Most of the refugees stuck in Greece are now women and children

Spring could bring a fresh surge of refugees. But Europe isn’t ready for them.

Turkey cracks down on foreign fighters