BRUSSELS — Turkey surprised European Union leaders on Monday by hitting them with a steep new set of demands as preconditions to help stem the flow of refugees from Syria and Iraq and other migrants seeking to enter Europe.

The demands at the start of an emergency summit in Brussels included billions in more money, easier access to visas for Turks to go to Europe, and the dramatic acceleration of talks on Turkey’s membership in the bloc, a discussion that has languished for years.

The toughening of the Turkish position came just days after the government seized Zaman, the country’s largest newspaper, as part of a media crackdown, and underscored Ankara’s seeming attempt to use the migration crisis to its advantage.

Human rights considerations were now likely to be trumped by the urgency of the migration crisis, as time runs down for the bloc to come up with a plan to head off a new surge of migrants in coming weeks.

The Turkish demands, in fact, laid bare the European Union’s weakening position and signaled that the difficulties — and costs — of managing the crisis may only rise the longer it stumbles on.

Hoping to avoid a repeat of last year, when hundreds of thousands of migrants overwhelmed authorities from Greece to Germany, and beyond, European leaders were weighing whether to declare “closed’’ the route migrants have taken through the Balkans to reach Western Europe.

But such a step threatens to bottle up migrants in already hard-pressed Greece, and has sharply divided European leaders, with Chancellor Angela Merkel of Germany suggesting that it would undo the Continent’s commitment to help those in need.

“You end up in situations like this when you have neglected to build the capacity to deal with the bigger issues of our time,’’ said Fredrik Erixon, the director of the European Center for International Political Economy, a research group in Brussels.

“Turkey now is going to raise the costs for Europe,’’ he added, “and to such an extent that Europe may not be able to oppose Turkish goals in the region including how to deal with Syria and the Kurds.’’

As the meeting got underway, Prime Minister Ahmet Davutoglu reiterated calls for the creation of a “safe zone’’ in Syria where migrants could be free from the violence that has torn the country apart over the last five years.

In a televised speech on Monday, Turkey’s president, Recep Tayyip Erdogan, said the country had spent $10 billion caring for the Syrian refugees. He said the EU had been slow to disburse the 3 billion euros it pledged.

Davutoglu surprised a handful of European leaders on Sunday night, in a negotiating session that dragged on until nearly 3 a.m., by putting Turkey’s attempts to join the EU— a process known as accession — on the agenda.

“Turkey is ready to work with the EU,’’ Davutoglu told reporters before the summit meeting on Monday. “Turkey is ready to be a member of the EU as well.’’ He added, “I hope this summit, which will not focus only on irregular migration but also on the Turkish accession process to the EU, will be a success story and a turning point in our relations.’’

Donald Tusk, the president of the European Council, which represents the leaders of the 28 nations that make up the EU, spent last week in the Balkans and in Turkey, in preparation for the Brussels meetings.

Last week, he sternly warned migrants who are seeking a better life in Europe, but are not eligible for political asylum, not to come, and Tusk’s staff drafted a statement declaring that leaders had decided to “close the Western Balkans route’’ that the migrants have used to reach destinations like Austria, Germany, and Sweden.

Merkel said on Monday that “we want to fight illegal immigration and that is only possible in cooperation with Turkey,’’ but she was said to resist the wording of Tusk’s statement.

However, Merkel, arguably the most influential of the leaders in shaping the European Union’s policies, appeared to be facing pressures from all around her.

She, in particular, is concerned about letting the migrants get trapped in Greece and about renewed turmoil there after a crippling debt crisis nearly forced the country out of the eurozone.

Germany also has been sharply at odds with its neighbor, Austria, after the government in Vienna imposed restrictions on the free flow of migrants, threatening the bloc’s system of passport-free travel.

“It cannot be that something will be closed,’’ Merkel was quoted by German news agency DPA as saying about the Western Balkans route ahead of the meeting.