The agency's report has been sent to Brussels as part of Italy's request to tap the EU Solidarity Fund to help pay for recovery efforts.
The estimate includes damage to homes and other privately-owned buildings, totalling 12.9 billion euros, and 1.1 billion euros of damage to public buildings.
The cost to repair artworks, monuments and other historic gems in the region, home to hundreds of medieval towns and villages, was set at three billion euros.
But the damage at the time was estimated at just seven billion euros.
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Since then, several powerful quakes have rocked the region, leaving thousands of people homeless for months at a time.
In one deadly episode, four earthquakes hit central Italy on January 18. About three hours later, an avalanche slammed into the Hotel Rigopiano, burying the structure in rock and snow and killing 29 people.
The European Commission had unblocked an initial 30 million euros on November 29, the maximum amount available while awaiting Italy's full estimate.
The country says the quakes, along with the influx of migrants seeking to enter Europe, are exceptional events that should allow the country to ease up on deficit reduction targets.
The EU had wanted Italy to reduce its deficit to 1.8 per cent of GDP, but Rome wanted to raise this to 2.3 per cent.
But it appears the Italian government has agreed to find an additional 3.4 billion of savings, to bring the deficit to 2.1 per cent of GDP.
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