BEIJING—Apple Inc. Chief Executive Tim Cook met Chinese government officials in Beijing Monday, a company spokeswoman said, as the consumer-electronics giant faces a legal challenge in China to the iPad trademark and as it looks to further its surging Chinese growth.

A spokeswoman said Mr. Cook— who is on his first trip to China since becoming chief executive of the Cupertino, Calif., company— "had great meetings with Chinese officials today."

"China...