Apple Inc. launched a new round in its charm offensive in China, announcing two additional research-and-development centers ahead of speeches Chief Executive Tim Cook is scheduled to give at a major Chinese government conference.

The new centers, to be set up in Shanghai and Suzhou, bring Apple’s total commitment to R&D facilities in China to more than 3.5 billion yuan, or about $500 million, the company said Friday in an announcement issued only in Chinese. Apple currently operates a center in Beijing and last year committed...