SHANGHAI  In an apparent bid to extend its control over the Internet and cash in on the rapid growth of mobile devices, China plans to create a government-controlled search engine.

The new venture would compete with Baidu.com, a private company that runs China’s dominant search engine. Baidu’s market has grown since Google retreated from the mainland earlier this year.

The state-owned China Mobile  the world’s biggest cellphone carrier  and Xinhua, China’s official state-run news agency, signed an agreement on Thursday to create a joint venture called the Search Engine New Media International Communications Company.

China already has the world’s largest number of Internet users, more than 420 million, and also the largest number of mobile phone subscribers, with more than 800 million.