Apple Inc. is pushing back the production ramp-up of its flagship iPhones coming later this year by about a month, according to people familiar with the changes, as the coronavirus pandemic weakens global consumer demand and disrupts manufacturing across Asia, the heart of the consumer electronics supply chain.

Apple is forging ahead with plans to release four new iPhone models later this year, people familiar with its plans say. The phones, some with 5G connectivity, will vary in price and come in three sizes—5.4 inches,...