The bodies were found on the 25-meter (82-foot) Ghareeb off the small island of Tilos, near Rhodes in the southeastern Dodecanese chain. Local fishermen discovered the yacht at about 9:30 a.m. (0630GMT) in the bay of Lethra, the Merchant Marine Ministry said.
A ministry spokeswoman said a crew list found on the vessel indicated the dead men were an Italian and a Filipino crewman. Police were looking for another Filipino national believed to have been the third crewman on board.
The identities of the three men were not immediately available.
One of the bodies was found on the yacht's deck, wrapped in a blanket, and the other in a cabin, shrouded in a bloodstained sheet.
"They bore wounds from a sharp instrument, possibly a knife," the Merchant Marine Ministry spokeswoman said, speaking on customary condition of anonymity. She said the vessel - which was traveling from Kusadasi in Turkey to Rhodes - had taken on water from a hole in the hull, and was close to sinking.
"We think the incident must have occurred in the past 24 hours at the most," she added.
Port officials arrived from other islands to investigate the incident, while police homicide experts was sent to Tilos from Athens. Police have also informed the anti-terrorism department.
Russia's Ambassador to Belarus, Mikhail Babich, said that Moscow would treat any military intervention in the affairs of Belarus as an attack on Russia