BEIJING (Reuters) - China's vice premier promised Apple <AAPL.0> Chief Executive Officer Tim Cook that the country would boost intellectual property protection, state media said on Wednesday, in Cook's second day of meetings in the company's biggest potential market.

China is the world's largest mobile market and already Apple's second-biggest market overall, but its growth there is clouded by issues ranging from a contested iPad trademark to treatment of local labor.

"To be more open to the outside is a condition for China to transform its economic development, expand domestic demands and conduct technological innovation," the official Xinhua news agency cited Vice Premier Li Keqiang as saying.

Apple is in a long-running dispute with Proview - a financially weak technology company that claims to have registered the iPad trademark. The legal battle is making its way through Chinese courts and threatens to disrupt iPad sales.

The company is also reviewing labor standards at the Taiwan firm which assembles its iPhones and iPads, Foxconn Technology Group, accused of improper practices in China.

Widely expected to become China's next premier in a leadership transition that begins later this year, Li called on multinational companies to "pay more attention to caring for workers" in China, Xinhua said.

Cook said Apple will conduct business in a law-abiding and honest manner, according to Xinhua.

Apple officials were not immediately available for comment.

Apple has begun releasing monthly labor data and said it reached 89 percent compliance with its 60-hour work week policy in February, up from 84 percent in January, according to a survey of 500,000 workers at suppliers worldwide.

Cook is on his first trip to the country since taking over from Steve Jobs in August. His closely guarded itinerary has included talks on Monday with Beijing's mayor and a visit to one of Apple's two stores in the capital.

Though it retails through more than 100 resellers, Cook has said Apple has merely scratched the surface in China, its biggest manufacturing hub where it has only five stores.

(Reporting by Michael Martina; Editing by Ron Popeski)