The oil rig was at the center of standoff between the countries in 2014 when China parked it near the Paracel islands, which Vietnam claims as its exclusive economic zone. The incident sparked deadly riots in Vietnam.
Foreign Ministry spokesman Le Hai Binh said China has moved the oil rig into an area in the Gulf of Tonkin where the countries are negotiating the demarcation of their sea border.
He said Vietnam had lodged a protest with the Chinese Embassy in Hanoi.
Binh also said China's operation of a new lighthouse on one of the seven artificial islands it has recently constructed in the South China Sea was "illegal and invalid."
Rejecting Vietnam's demands, Chinese Foreign Ministry spokesman Hong Lei said the oil rig is conducting standard exploratory activities within waters under China's "undisputed" jurisdiction.
Hong also said the operation of the lighthouse on Subi Reef is a matter falling within China's sovereignty.
The lighthouse is intended to "better fulfill China's international responsibilities and obligations and provide more public facilities to the regional countries, so as to maintain freedom and safety of navigation in the South China Sea," Hong said.
The relocation of the Chinese oil rig last Sunday came just days before Vietnam's legislature swore in new Prime Minister Nguyen Xuan Phuc, who has vowed to defend Vietnamese sovereignty.
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