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The figure is less than half the 5.2 billion euro shortfall recorded in January 2012, the national statistics office ISTAT said, issuing preliminary estimates.
Exports surged by 17.7 percent and imports fell back 5.6 percent compared with a year earlier, it said.
Leaving energy products aside, the trade balance was positive at 2.9 billion euros, compared with 869 million euros in January 2012, thanks mainly to strong sales of equipment for businesses and services.
Compared with December 2012, exports were up 3.9 percent and imports by 3.0 percent, ISTAT said.
A trade surplus is one of the factors of growth in an economy.