Three people died and another 28 were admitted to hospital on the island of Crete after they were found on a beach near where two ships carrying migrant workers evacuated from Libya arrived.
The Merchant Marine Ministry said it was checking whether the 31 men, mainly from Bangladesh, had jumped overboard from two ships that docked in Crete with a total of about 2,000 evacuees from Libya, in an attempt to avoid being transferred home.
Ships have been ferrying thousands of evacuees from Libya to Crete in recent days.
The ministry said coastguard officials called to a beach near Souda Bay found the 31 men, all soaking wet. Three were dead, while many of the others were suffering from hypothermia.