It would mark the third straight quarterly rise.
The ministry estimated crude steel output at 24.11 million tonnes for three-month period, up from 21.99 million tonnes a year earlier, reflecting a pick-up in demand in areas such as auto manufacturing and industrial machinery.
It expected steel output to rise 0.8% from the July-September quarter.
Demand for steel products, including those for exports, is forecast to increase 6.7% to 21.84 million tonnes in October-December versus a year earlier, the ministry said, citing an industry survey.
Exports are forecast to jump 16.9% to 7.11 million tonnes, the ministry said.
However, it warned of an increased risk of a downturn due to the impact of the coronavirus pandemic on supply chains and said close attention was needed on the trend of COVID-19 infections at home and abroad.
Japan's industrial output fell for a second straight month in August as COVID-19 outbreaks elsewhere in Asia disrupted supply chains for carmakers already facing headwinds from a prolonged chip shortage.
Major Japanese automakers including Toyota Motor Corp, Nissan Motor Co and Honda Motor Co have suffered production cuts since late August due to a components shortage, which could last well into October, the industry lobby warned earlier last month.
(Reporting by Yuka Obayashi; editing by Clarence Fernandez and Richard Pullin)
By Yuka Obayashi
