* CSI300 -1.2 pct; SSEC -1.1 pct; HSI -0.5 pct
* China manufacturing data contracts at the fastest pace in 3 yrs
* Investors shrug off fresh policies to support real estate, M&A
SHANGHAI, Sept 1 (Reuters) - Chinese stocks gyrated wildly on Tuesday, with main indexes tumbling 5 percent at one point as weak manufacturing data laid bare the daunting challenge faced by Beijing as it races to revive a stumbling economy.
At the end of the morning session, the markets had managed a recovery of sorts, with the CSI300 index off 1.2 percent to 3,324.83 points, while the Shanghai Composite Index was off 1.1 percent, to 3,172.03 points.
Hong Kong stocks also fell, weighed down by weak retail sales data, and sluggish performance on Wall Street.
Markets, which have endured a torrid August month, were hit hard again on renewed fears of a China-led slowdown in global growth.
Those concerns played out once more after surveys showed a further loss of momentum in China's giant economy.
Activity in China's manufacturing sector contracted at its fastest pace in three years in August, an official survey showed on Tuesday, reinforcing fears of a sharper slowdown in the world's second-largest economy. A separate private survey on manufacturing was equally downbeat.
Investors largely ignored fresh stimulus measures unveiled by the government, including further relaxation in property investment rules, and policies to support mergers and acquisitions and share buy-backs by listed companies.
Du Changchun, analysts at Northeast Securities in Shanghai, said that many investors, worried about the economy, choose to stand on the sidelines.
Stimulus policies "are more likely to help the economy instead of the stock market, and it takes some time for these measures to take effect.
"Investors have little willingness to get into the market."
Most sectors fell but an index tracking banking shares erased early losses and was up 1.2 percent by midday, as the previous days' correction attracted bargain hunting.
Also bucking the trend are oil giants PetroChina and Sinopec, both up over 3 percent after a recent surge in global oil prices.
Small caps posted heavy losses. Shenzhen's growth board ChiNext and the CSI500 index of small companies both tumbled over 3 percent.
Bright Dairy & Food Co slumped 5.2 percent, adding to Monday's 4.8 percent fall, after the company reported weak earnings, and was downgraded by Credit Suisse.
In Hong Kong, the Hang Seng index dropped 0.5 percent, to 21,569.14 points, while the Hong Kong China Enterprises Index lost 1.3 percent, to 9,620.06.
Hong Kong retail sales fell for the fifth straight month in July, as a slowdown in tourist arrivals further battered sales of big-ticket items such as jewellery and watches, while a plunge in the stock market hurt consumer sentiment.
Most major sectors fell in the city. (Samuel Shen and Pete Sweeney; addition reporting by Shanghai Newsroom; Editing by Shri Navaratnam)