Over one million people have watched the video, many of whom are saying the cat is "so cute."
One vessel went down near the southern Greek island of Folegandros on Tuesday night, and a sailboat sank off the country's southern coast on Thursday.
"Efforts will continue but in waters that are very cold and very deep the chances of finding anyone [alive] are decreasing by the hour," a spokesman said.
Kushila Stein was found floating in the Aegean Sea 55 nautical miles north of Heraklion in Crete.
The gruesome execution took place 2,000 years ago on the Greek island of Thasos.
The Turkish Coast Guard rescued nine people and recovered five bodies.
Germany said it would take part, along with Greece and Turkey, and the U.S. supports the plan.
Nearly 400 people have drowned trying to cross from Turkey to Greece by boat this year.
More than 200 people have drowned trying to reach Greece from Turkey this year.
Half of the arrivals are fleeing war in Syria, according to the U.N.
More than 3,500 people have died or gone missing at sea this year.
The boat carrying the 18-month-old capsized in the Aegean Sea.