HONG KONG, Dec 13 (Reuters) - China stocks snapped a three-day rally on Wednesday while Hong Kong shares also declined, as the key messages at the Central Economic Work Conference focusing on defusing risks but lacking new property stimulus, fails to excite investors.

** The blue-chip CSI 300 Index fell 0.9%, while the Shanghai Composite Index slipped 0.5%.

** Hong Kong's Hang Seng Index dropped 0.7% and the Hang Seng China Enterprises Index lost 1%.

** Broader Asian shares were subdued, as traders awaited this year's final policy decision from the Federal Reserve and clues on whether the U.S. central bank would cut rates next year.

** China will focus on boosting effective demand next year, and make concerted efforts to spur domestic demand, state media said, citing the annual Central Economic Work Conference held from Dec. 11-12.

** Analysts said the agenda-setting meeting of the country's top leaders show less focus on the property sector, while pays more attention to domestic demand, which is within market's low expectation.

** While policymakers acknowledged economic challenges and maintained pro-growth tone, "there is no new statement around property" in the readout, said Goldman Sachs analysts in a note.

** Citigroup Inc analysts expect December property sales to remain weak.

** Meanwhile, a senior Communist Party official told state media CCTV that China should set its 2024 fiscal deficit and special local government bonds at appropriate levels and optimise the structure of fiscal spending. The comments were made after the agenda-setting meeting.

** Most sectors went down with liquor and real estate stocks falling 2.9% and 2.5%, respectively, to lead the decline.

** Hong Kong-listed tech giants dipped 0.8%.

(Reporting by Summer Zhen; Editing by Rashmi Aich)