BRUSSELS — The day before a European conference designed to persuade Turkey to curb the uncontrolled flow of migrants making perilous journeys across the Aegean Sea, NATO announced on Sunday that it would expand its maritime efforts to stop the smugglers who make many of those journeys possible.

More than one million migrants arrived in Europe last year, and the prospect of another large influx threatens to overwhelm Greece and destroy a policy of open borders across much of the Continent.

The dangers faced by migrants who take sea routes to Greece were underscored again on Sunday when at least 18 people drowned off the Turkish coast, according to news reports. More than 300 migrants have already died this year making similar journeys on that route.

As part of efforts to quell the mounting crisis, Jens Stoltenberg, the secretary general of NATO, said Sunday that ships used by the alliance would begin conducting operations in the territorial waters of Greece and Turkey after “close consultation and coordination” with the two countries.

Last month, Mr. Stoltenberg said NATO forces would “not turn back the boats.” But, he added, if NATO vessels did “encounter people in distress at sea,” the crews would live up to their “responsibility to assist.”

European Union leaders, such as Chancellor Angela Merkel of Germany, want to persuade Turkey to reduce the number of migrants leaving its shores and to take back large numbers of people who have already crossed the Aegean but are not eligible for political asylum in Europe.

In exchange, European countries would offer to directly resettle a large number of refugees living in camps in Turkey who have fled the violence in Syria. In addition, the European Union could eventually add to the $3.3 billion it pledged to Turkish aid organizations in November. That money was intended to help manage millions of refugees and migrants in Turkey.

European Union leaders had raised hopes that such a trade-off with the Turkish prime minister, Ahmet Davutoglu, could be negotiated at the meeting in Brussels on Monday. They have said, however, that it remains too early for an agreement on the number of people who would be transferred from Europe back to Turkey.

Another factor that could impede progress at the meeting is a ruling by a Turkish court ordering the seizure of the opposition Zaman newspaper.

That move has prompted sharp criticism from some European Union parliamentarians who say Europe relies too heavily on Turkey to ease the migration crisis. They say it should instead make a unified effort to help Greece and create an effective coast guard to protect the bloc’s coastlines.

In Greece, a nation still grappling with severe economic problems, many thousands of migrants have become trapped because Macedonia, which is not a member of the European Union, has blocked their passage northward.

On Sunday, Guy Verhofstadt, the leader of the Alliance of Liberals and Democrats group in the European Parliament, said Turkey had so far given little more than “empty promises” on returning migrants. He also warned against making a deal with “a country that imprisons journalists, attacks civil liberties and with a highly worrying human rights situation.”

As Europe continues to dither over the worst crisis of its kind since the Second World War, the announcement that NATO would expand its operations could, at least, give leaders more time to reach a more united position and wring more concessions from Turkey.

“Beefing up the NATO mission in the Aegean is going to help European leaders like Ms. Merkel claim that there’s progress bringing the situation under control,” said Mujtaba Rahman, the Europe director for the Eurasia Group, a political risk consultancy.

“But NATO is not the answer, so that means this really is about buying yet more time to reach some kind of solution where Turkey shows a willingness to keep refugees from leaving its shores in the first place,” Mr. Rahman said.