The United States is investigating the recent movement of a massive Chinese oil rig that Vietnam says is now in its waters.

The Vietnamese complaint comes after US President Barack Obama visited the region in a demonstration of the US's ties with a number of allies, including Japan and South Korea.

Vietnam condemned the Chinese rig's operation in what it claims are its waters in the South China Sea and demanded that the Chinese state oil company remove it.

China responded by saying the rig is actually operating wholly within its waters.

Daniel Russel, Assistant Secretary of State for East Asian and Pacific Affairs, told Reuters that all sides should show caution.

"We believe that it is critically important for each of the claimant countries to exercise care and restraint," he said.

"The global economy is too fragile and regional stability is too important to be put at risk over short term economic advantage," he added.

During Barack Obama's presidency, the US has trumpeted a 'pivot to Asia,' as the White House seeks to counter China's growing influence in the region. However, the so-called pivot has yet to materialise, as the US Secretary of State John Kerry has been side-lined with complicated diplomatic pushes in the Middle East.

China claims nearly all of the territory in the South China Sea, rejecting rival claims from Vietnam, the Philippines, Taiwan, Malaysia and Brunei. The country with the world's second largest economy is also embroiled in a bitter dispute with Japan over contested islands.

China's Maritime Safety body warned on Saturday that all vessels should remain one mile away from the rig. The exclusion zone was expanded to three miles on Monday.

The rig is owned by China's state-owned CNOOC oil company and is valued at $1bn. It was previously drilling south of Hong Kong, before being moved to its current, disputed location.