KYTHIRA, Greece — A jarring public-awareness ad that has appeared recently on Greek television news shows a little girl strolling with her mother through the National Archaeological Museum in Athens, one of the country’s cultural crown jewels. The girl skips off by herself, and as she stands alone before a 2,500-year-old marble statue, a hand suddenly sweeps in from behind, covering her mouth and yanking her away.

An instant later, she reappears, apparently unharmed but staring forlornly at an empty plinth: The kidnappers weren’t after the girl — they were after the statue.

The ad, produced by the Association of Greek Archaeologists, is most immediately a reminder of an armed robbery of dozens of artifacts from a museum in Olympia in February, amid persistent security shortcomings at museums across the country. But the campaign’s central message — “Monuments have no voice. They must have yours” — is a much broader attack on deep cultural budget cuts being made as part of the austerity measures imposed on Greece by the European economic establishment, measures that have led in recent weeks to an electoral crisis, a caretaker government and the specter of Greece’s departure from the euro zone....