A government statement today said Vietnamese Foreign Minister Pham Binh Minh told Chinese State Councillor Yang Jiechi that Hanoi would "apply all necessary and suitable measures to defend its rights and legitimate interests" in relation to the rig.
The development represents an escalation of the dispute, and is a sign of Vietnam's anger over China's actions.
Beijing previously said the rig is in its territorial waters.
China claims most of the oil- and gas-rich South China Sea as its own, putting it into conflict with Vietnam, the Philippines and several other nations that claim parts of the sea.