Samsung Electronics Co. is building the world’s largest phone factory in India in an effort to tap the industry’s next growth area: cheap smartphones.

After waging a decadelong battle with Apple Inc. for the world’s most affluent consumers, the South Korean electronics giant is now looking to fend off Chinese companies trying to dominate the market for inexpensive phones. That market is twice the size of the high-end market but offers lower profitability.

India...