By Greg Torode

HONG KONG (Reuters) - China has warned Vietnam not to disturb activities of Chinese companies operating near disputed islands in the South China Sea, after Hanoi condemned as illegal the movement of a giant Chinese oil rig into what it says is its territorial water.

The United States on Tuesday sharply criticized the movement of the deep sea oil rig, calling it "provocative and unhelpful to the maintenance of peace and stability in the region".

The relocation of the oil rig by China's state-run oil company is the latest show of Beijing's growing assertiveness, which is raising alarm among smaller countries in the region.

China's State Councilor Yang Jiechi told Vietnam's deputy prime minister and foreign minister, Pham Binh Minh, that Chinese firms operating in the Paracel Islands, which the Chinese call the Xisha Islands, are within the mandate of China's sovereignty and should not be subject to interference, according to a statement posted on the Chinese foreign ministry's website late on Tuesday.

Vietnamese harassment of Chinese companies conducting normal activities violated China's sovereignty and administration rights, Yang, the country's top diplomat, said in a telephone call to Minh.

The incident came days after U.S. President Barack Obama visited Asia to underline his commitment to allies there, including Japan and the Philippines who are themselves locked in territorial disputes with China.

Obama, promoting a strategic "pivot" toward the Asia-Pacific region, also visited South Korea and Malaysia, but not China.

Daniel Russel, Assistant U.S. Secretary of State for East Asian and Pacific Affairs, said the United States was looking into the oil rig matter, but urged caution from all sides.

"We believe that it is critically important for each of the claimant countries to exercise care and restraint," he told Reuters during a visit to Hong Kong ahead of a previously scheduled trip to Hanoi on Wednesday.

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

China claims almost the entire oil- and gas-rich South China Sea, rejecting rival claims to parts of it from Vietnam, the Philippines, Taiwan, Malaysia and Brunei. It also has a separate maritime dispute with Japan.

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Its claims coincide with growing diplomatic and military influence in the region and have raised fears of possible conflict.

The Maritime Safety Administration of China (MSAC) announced on its website on Saturday that all vessels should keep one mile (1.6 km) away from the rig, called the Haiyang Shiyou 981. It expanded that to three miles on Monday.

The $1 billion rig is owned by China's state-run CNOOC oil company and it had been drilling south of Hong Kong.

On Sunday, Vietnam's Foreign Ministry spokesman objected to the Chinese announcement, saying the coordinates of the oil rig put it in Vietnam's exclusive economic zone and on its continental shelf, about 120 nautical miles off its coast.

The spokesman, Le Hai Binh, said in a statement Vietnam "resolutely opposed" the Chinese company's drilling.

But, like other Asian nations involved in territorial disputes with China, Vietnam appears to have limited options when dealing with the emerging superpower.

The Philippines said last month that the United States had a treaty obligation to help in case of an attack on its territory or armed forces in the South China Sea, although Obama did not say categorically that Washington would do so.

In 1992, Vietnam sent naval vessels into an area where China signed a contract with a U.S. firm to develop oil and gas in what it said were its waters.

"From 1992 until now, I haven't seen any action from Vietnam stronger than that," said a Vietnamese academic who specializes in South China Sea affairs.

"...My guess is either this action from China is to send a message to the United States after Obama's Asia visit, or to direct the community to this topic to distract them from the terror in Xinjiang."

China's nervousness about Islamist militancy has grown since a car burst into flames on the edge of Beijing's Tiananmen Square in October and 29 people were stabbed to death in March in the southwestern city of Kunming.

The government blamed militants from the far-western region of Xinjiang for both attacks.

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