The all-industry production index rose 3.0 percent from August, reversing a 1.2 percent decline a month earlier, according to the Ministry of Data and Statistics.
Mining and manufacturing output jumped 9.0 percent, while manufacturing production rose 9.9 percent.
Semiconductor production surged 19.2 percent from the previous month and automobile output jumped 39.9 percent. Pharmaceutical production also increased 20.6 percent.
Services output rose 0.5 percent, led by wholesale and retail and transportation and storage.
Retail sales increased 3.6 percent from August as sales of food and beverages, cosmetics and passenger cars rose.
The rebound, however, followed declines in both July and August. Retail sales remained 0.4 percent lower than a year earlier.
Facility investment rose 5.3 percent from the previous month, supported by machinery and transport equipment.
Investment was 10.1 percent higher from a year earlier, led by a 22.2 percent increase in machinery including semiconductor-manufacturing equipment.
Construction activity increased 5.8 percent on month as both building and civil engineering work rose, although it remained 1.6 percent lower than a year earlier.
The cyclical component of the coincident composite index, which tracks current economic conditions, rose 0.5 point from August. The corresponding leading index slipped 0.1 point.
On a quarterly basis, all-industry production rose 1.9 percent in the July-September period, while mining and manufacturing output increased 3.9 percent and facility investment gained 6.3 percent.
Retail sales, however, fell 1.0 percent from the previous quarter, indicating that September's monthly rebound has yet to translate into a broader recovery in household spending.
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