SHANGHAI, Jan 8 (Reuters) - China stocks closed slightly lower on Friday, with the blue-chip CSI300 index retreating from a 13-year high, as investors booked profits following a six-session rally amid worries over Sino-U.S. tensions. ** The CSI300 index fell 0.3%, to 5,495.43, while the Shanghai Composite Index shed 0.2%, to 3,570.11. ** The tech-heavy start-up board ChiNext eased 0.4%, while the STAR50 index slipped 0.2%. ** For the week, CSI300 gained 5.5% and SSEC added 2.8% as investors cheered data and survey pointing to a continued recovery in the world’s second-largest economy. ** Trump administration officials are expected to discuss a proposed expansion of an executive order banning U.S. investment in alleged Chinese military companies at a Thursday afternoon meeting. ** The U.S. ambassador to the United Nations, Kelly Craft, will visit Taiwan on Jan. 13-15 for meetings with senior Taiwanese officials, the U.S. mission to the U.N. said on Thursday, prompting China to warn they were playing with fire. ** Leading the decline on Friday, the CSI300 consumer staples index dropped 3%. Despite session’s losses, the index is still up 8% this year. ** The CSI new energy index, tracking China’s high-flying new energy sector, retreated 1.9%. The index has gained 9.6% this year, following a 105% rise in 2020 thanks in part to China’s carbon neutrality pledge. ** “There are signs of crowded trade in some hot sectors for now as investors expect more fund inflows via mutual funds,” said Jin Jing, an analyst with Caitong Securities. ** Jin also noted the weakness in small-cap stocks since China published new delisting rules. ** Late last year, China’s exchanges published new rules for simplifying the delisting process for public companies. (Reporting by Shanghai Newsroom; Editing by Subhranshu Sahu)