(Adds China arranging two more flights in second paragraph, foreign ministry spokesman's quote, travel advice in paragraphs 13,14)
HANOI, May 18 (Reuters) - Vietnam flooded major cities with police to avert anti-China protests on Sunday, while Beijing evacuated thousands of citizens after a flare-up over disputed sovereignty in the South China Sea sparked rare and deadly rioting in Vietnam last week.
China has evacuated more than 3,000 nationals following the attacks on Chinese workers and Chinese-owned businesses at industrial parks in its southern neighbour.
On Sunday, China arranged two chartered flights to bring nearly 300 people, many of them injured, home to its southwestern city of Chengdu, while five ships were on their way to Vietnam to bring out more people, state-run Xinhua news agency reported.
Sixteen critically injured were evacuated separately, aboard a chartered medical flight in the morning, China's foreign ministry said.
Several arrests were made in the capital Hanoi and commercial hub Ho Chi Minh City within minutes of groups trying to start protests, according to witnesses, as Vietnam's communist rulers stuck to their vow to thwart any repeat of last week's violence in three provinces in the south and centre.
Fury has gripped Vietnam after Chinese state energy firm CNOOC deployed dozens of ships two weeks ago and towed a $1 billion oil rig to a location 240 kilometres (150 miles) off Vietnam's coast in an area both counties claim.
It was one of the most assertive moves China has made in seas believed to be endowed with billions of barrels worth of oil.
Coming just days after U.S. President Barack Obama visited several Asian allies engaged in territorial disputes with China, and U.S. official in Washington described China's action as provocative, and said Beijing's fraught relations with neighbours could potentially strain ties with the United States.
"Our intention was to protest in support of the government to chase the oil rig away from Vietnam's territorial waters," said Van Cung, 74, a retired army colonel who was attempting to protest outside the Chinese embassy in Hanoi.
Protests of hundreds in Vietnam's cities were allowed to a week ago, a rare move in a state that usually suppresses them. However, what started as a peaceful march in two southern industrialised provinces on Monday spiralled a day later into a rampage of arson, destruction and looting of Chinese-owned factories, and Taiwanese businesses mistaken for being Chinese.
Fighting between Vietnamese and Chinese workers broke out in central Ha Tinh province on Wednesday killing two people and wounding 140, the government said. China's foreign ministry also put the casualties at two dead and 100 injured, Xinhua said.
A doctor and an eyewitness, however, said they saw between 13 and 21 dead bodies, mostly Chinese, on the night of the unrest.
"The severe violence targeting foreign companies in Vietnam since May 13 has caused casualties and property losses for Chinese nationals. This has destroyed the atmosphere and conditions for bilateral communication and cooperation," Chinese Foreign Ministry spokesman Hong Lei said on Sunday.
The ministry also upgraded its travel advice for Vietnam on Sunday, telling Chinese citizens "not to go for the time being".
China has demanded swift action against the perpetrators and for Vietnam to do more to protect Chinese nationals and businesses.
A text message was sent to Vietnamese cellphone users on Saturday saying Vietnam's Prime Minister Nguyen Tan Dung had ordered the security forces to prevent illegal acts. A top police investigator rejected assertions that the authorities remained aloof when the rioting erupted.
Police and traffic police gathered in small clusters on street corners in the centres of Hanoi and Ho Chi Minh City on Sunday, where large numbers of people were milling around in hot and humid conditions in anticipation of rallies.
Trucks with loudspeakers circled parks and stopped at intersections telling onlookers to disperse. A handful of people who tried to start a protest in Ho Chi Minh City were rounded up and taken away in a van as sirens blared.
"Vietnam may be small, but we are not weak", said a small sign held up by a man who was ordered by police to disperse.
The spat has been the worst breakdown in shaky but important ties between the two Communist states since a brief but bloody border war in 1979.
Trade between the two neighbours was worth $50 billion last year, with China a crucial source of imports for Vietnam. Diplomatic ties have long been strained and many Vietnamese are embittered by what they see as a history of Chinese bullying.
The rioters had also targeted Taiwan and Hong Kong businesses, presumably mistaking them for mainland Chinese. On Sunday, Singapore issued a statement saying Vietnam's Foreign Minister Pham Binh Minh had called his Singaporean counterpart to give assurance that industrial parks for joint ventures between the two countries would be protected.
Vietnam's authorities have long been uncomfortable with public protests, even if they are about China, in what is often seen as fear that demonstrations could harness wider discontent over land grabs, corruption, an underperforming economy and one-party rule.
Dao Minh Chau, 44, who described himself as "a Vietnamese who loves his motherland", said he was fully behind the government.
"We already signed a letter to request the government to bring China to the international courts," he said.
"We will tell clearly to our government that we behind the government to protest China's aggressive policy and the government can rely on us." (Additional reporting by Sui-Lee Wee; Writing by Martin Petty; Editing by Simon Cameron-Moore)