The Greek coastguard apprehended 67 refugees, most of them men, aboard a sailboat off the eastern Aegean island of Amorgos on Wednesday.
"The migrants started out from Turkey and wanted to travel directly to the Greek mainland," a coast guard official told dpa.
Among the sailboat passengers were 60 men, five women and two children.
In Cyprus, police discovered 15 refugees on an isolated beach who had been brought there in a speedboat by human traffickers from the Turkish coast some 74 kilometres away, according to authorities in Nicosia.
Migrants who disembark on Greece's eastern Aegean Islands are not allowed on the mainland. They must instead wait several months until their asylum applications are accepted or otherwise face deportation back to Turkey.