SHANGHAI, Feb 2 (Reuters) - China stocks fell on Friday, with the Shanghai share benchmark heading for the worst week in five years, as authorities' policy support measures so far have failed to excite investors and bring a sustained rally, amid the country's still weak economic fundamentals.

Hong Kong shares, meanwhile, rose slightly, lifted by index heavyweight Tencent Holdings after China approved licences for games by the social media and gaming giant.

** The blue-chip CSI300 Index and the Shanghai Composite Index both lost 0.7% by the midday recess. So far this week, the Shanghai Composite is down 5.5%, on course for the biggest weekly decline since April 2019.

** Hong Kong's Hang Seng Index added 0.6% and the Hang Seng China Enterprises Index climbed 0.8%.

** Other Asian shares were buoyed by a late bounce in U.S. tech as results from Meta and Amazon beat expectations, while investors are bracing for U.S. jobs figures, which could hasten bets for rate cuts if they come in below forecast.

** "Investor sentiment has stagnated since last week's temporary excitement about potential policy shift," said Morgan Stanley in a note.

** China's stock market logged a strong weekly performance last week, backed by a string of supportive policies by Beijing, including a deep cut to bank reserves.

** "Market sentiment likely to stay range bound in the near term amid lukewarm macro data and quieter policy cycle ahead of holidays," Morgan Stanley said. "Under continuous deflationary pressure and its potential implications on cooperate earnings, we have lowered our China market 2024 index target prices."

** Shares in healthcare, information technology , securities, new energy shares slumped more than 2% each.

** China approved licences for 32 imported online games for 2024, including two titles to be published by Tencent, according to the press and publication administration.

** Tencent jumped 3.2% in Hong Kong, boosting the Hang Seng Tech Index up 0.4%.

** China's central bank issued 150 billion yuan ($21 billion) in loans to policy banks through its pledged supplementary lending (PSL) facility in January, granting such loans for a second month as part of a push to support its "urban village" plan.

** The Hang Seng Mainland Properties Index jumped 2.6%.

(Reporting by Shanghai Newsroom; Editing by Sohini Goswami)