CNOOC Ltd. (CEO), China's top offshore oil producer, said Thursday that it began commercial production at two offshore oil fields in the South China Sea.

The Weizhou 11-2 and Weizhou 6-9/6-10 fields are located in shallow water in the Beibu Gulf, it said in a statement.

The Weizhou 11-2 field is expected to reach peak output of 3,960 barrels a day in 2012, while the Weizhou 6-9/6-10 field is expected to reach peak output of 5,870 barrels a day in 2013, CNOOC added.

CNOOC is the sole owner and operator of both fields, it said.

Although the Beibu Gulf is situated between Vietnam and China's Hainan island, it isn't clear where the fields are located. China is involved in a number of disputes with Southeast Asian nations over offshore drilling rights in the South China Sea.