SAN FRANCISCO — After months of delays, Apple is likely to open its first retail stores in India, a fast-growing market for smartphones where the American technology giant has little presence.

New rules issued by the Indian government on Monday exempt foreign-owned companies that want to open stores selling a single brand of products from requirements that 30 percent of the content of those products come from India. The exemption, which lasts three years, can be extended to eight years in the case of companies selling “cutting edge” items, such as Apple’s iPhones and Macs.

Apple, which makes virtually all of its devices in China, lobbied for months for the loosening, and Timothy D. Cook, the company’s chief executive, discussed it with government officials during his first visit to India last month.

An Apple spokesman declined to comment on the issue on Monday. The company has not yet received any formal response from the Indian government on its application to open stores.