SOUROTI, Greece—Legend has it that nearly three decades ago, a bearded Orthodox Christian mystic visiting here made an unsettling prediction: Greece in the future would experience a "great disruption and confusion," followed by hunger and political turmoil.

Believers say this grim vision of Elder Paisios, an ascetic monk who died in 1994, was actually a prescient glimpse of the upheaval now gripping this debt-racked country—helping fuel a surge of interest in the Orthodox holy man by Greeks struggling to make sense of a brutal...