NEW DELHI—Ikea Group took a significant step Tuesday toward setting up wholly owned stores in one of the furniture retailer's largest untapped markets, as India's foreign investment board forwarded the Swedish company's proposal to the federal cabinet.

Economic Affairs Secretary Arvind Mayaram said the Foreign Investment Promotion Board has cleared Ikea's proposal to invest €1.5 billion ($1.9 billion) to set up 25 stores in India.

The...