A fuel-economy testing scandal broadened in Japan on Wednesday, with Mitsubishi Motors Corp. saying its president would resign to take responsibility for overstating mileage in some cars and Suzuki Motor Corp. admitting to improperly testing its vehicles.

The moves by two of Japan’s second-tier car makers, both grappling with fierce competition and limited research-and-development budgets, came after Mitsubishi admitted to manipulating fuel-economy-related data and using an illegal testing method for multiple models in Japan....