SHANGHAI, Jan 4 (Reuters) - China and Hong Kong stocks fell on Tuesday morning, dragged down by technology shares, as Beijing's new cybersecurity rules damp sentiment, despite a rebound in property plays.

** China's blue-chip CSI300 index fell 0.8% by the lunch break, while the Shanghai Composite Index lost 0.4%.

** The Hang Seng index dropped 0.3%, and the Hong Kong China Enterprises Index lost 0.5%.

** China's cyberspace regulator said it would implement new rules from Feb. 15 that require platform companies with data for more than 1 million users to undergo a security review before listing their shares overseas.

** The Hang Seng Tech Index fell 1.4% at the end of the morning session, erasing early gains, as China's continued clampdowns on the tech sector sour market mood.

** Tech shares also fell sharply in China. The Nasdaq-style STAR Market lost 2.2%, while the start-up market ChiNext dropped 1.3%.

** But property shares in China and Hong Kong rebounded sharply, as the sector witnesses elevated volatility on debt repayment worries.

** The Hang Seng Mainland Properties Index bounced 4.4% in morning trade, after a 2.8% decline on Monday.

** China's CSI300 Real Estate Index rose 2%.

** Cash-strapped property developer China Evergrande Group said its contract sales dropped nearly 40% last year, and it will actively maintain communication with creditors. Its Hong Kong-listed shares, which were suspended on Monday, will resume trading on Tuesday afternoon.

** Chinese telecommunication stocks, including China Telecom , China Unicom and China Mobile, rose, ahead of China Mobile's Shanghai listing on Wednesday.

** China Mobile sold 845.7 million shares at 57.58 yuan ($9.06) each in Shanghai, representing a 50% premium to its Hong Kong share price. (Reporting by Shanghai Newsroom; Editing by Rashmi Aich)