ATHENS—Of all the challenges Greece has faced in recent years, prodding its citizens to pay their taxes has been one of the most difficult.

At the end of 2014, Greeks owed their government about €76 billion ($86 billion) in unpaid taxes accrued over decades; the government says only €9 billion of that can be recovered, with most of the rest lost to insolvency.

Billions more in taxes are owed on never-reported revenue from Greece’s vast underground economy, which was estimated before the crisis to equal more than a quarter of the country’s gross domestic product.

The International Monetary Fund and Greece’s other creditors have argued for years that the country’s debt crisis could be largely resolved if the government just cracked down on tax evasion. Tax debts in Greece equal about 90% of annual tax revenue, the highest shortfall among industrialized nations, according to the Organization for Economic Cooperation and Development.

Greece’s new government, scrambling to secure another tranche of short-term funding, agreed on Tuesday to make tax collection a top priority on a long list of measures. Yet previous governments have made similar promises, only to fall short.

Tax rates in Greece are broadly in line with those elsewhere in Europe. But Greeks have a widespread aversion to paying what they owe the state, an attitude often blamed on a combination of cultural and historical forces. During the country’s centuries-long occupation by the Ottomans, avoiding taxes was a sign of patriotism. Today, that distrust is focused on the government, which many Greeks see as corrupt, inefficient and unreliable.

“Greeks consider taxes as theft,” said Aristides Hatzis, an associate professor of law and economics at the University of Athens. “Normally taxes are considered the price you have to pay for a just state, but this is not accepted by the Greek mentality.”

An expanded version of this story is available at WSJ.com.