YICHUAN, China—Depositors swarmed a rural bank here for a third consecutive day, rushing to pull money out even as authorities stepped in forcefully to quell concerns around the latest troubled Chinese lender.

Local cadres, business leaders and banking executives rallied Thursday at the main branch of Henan Yichuan Rural Commercial Bank, just outside the central Chinese city of Luoyang. One by one, they stood before a microphone to pledge their backing for the bank, as smiling employees brandished wads of cash before television...