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.