China dismissed the objections, saying the activity was being carried out in its territorial waters.
Beijing's increasingly assertive territorial claims to the waters, which are thought to have large oil and gas deposits beneath them, have angered Vietnam, the Philippines and other claimants. The region is widely seen as a potential area of conflict.
Last week, President Barack Obama signed a new defence pact with the Philippines aimed at reassuring Asian allies of American backing as they wrangle with Beijing's growing economic and military might.
China's maritime administration also said that ships entering a 3-mile (4.8-kilometres) radius around the area are prohibited.
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Vietnam's foreign ministry said the area where the rig was stationed lay within Vietnam's exclusive economic zone and continental shelf as defined by the 1982 U.N. Convention on the Law of the Sea.
Vietnam's state-owned oil company, PetroVietnam, demanded that China National Offshore Oil Corporation "immediately stop all the illegal activities and withdraw the rig from Vietnamese waters."
Asked about Vietnam's objections, Chinese Foreign Ministry spokeswoman Hua Chunying said the drilling was taking place in Chinese waters.
Many analysts believe China is embarking on a strategy of gradually pressing its claims in the water by seeing what it can get away with, believing that its much smaller neighbours will be unable or unwilling to stop them. Vietnam has accused Chinese ships of cutting cables to its exploration vessels and harassing fishermen, as has the Philippines.