AHMEDABAD, India, Jan 17 (Reuters) - Indian automaker Maruti Suzuki will invest 350 billion rupees ($3.9 billion) in a plant it plans to set up in the western Indian state of Gujarat, the state's government said on Saturday.

The plant will add production capacity of up to 1 million vehicles a year for the automaker as it expands manufacturing to meet rising demand in India, the world's third-largest car market, and for exports, Gujarat said in a statement.

Production at the plant is expected to begin in financial year 2029 and will add to the annual production capacity of 2.4 million vehicles for Maruti, which is majority-owned by Japan's Suzuki Motor and is India's top carmaker by sales.

The company has an order backlog of about one and a half months for its entry-level models, its marketing and sales head, Partho Banerjee, said this month. The company said its sales to domestic dealers rose 37% in December to a record 178,646 units.

Maruti's board of directors this week approved an initial investment of 49.6 billion rupees to acquire land for the plant.

($1 = 90.6820 Indian rupees)

(Reporting by Sumit Khanna in Ahmedabad; writing by Ira Dugal in Mumbai; Editing by William Mallard)