SHANGHAI, May 27 (Reuters) - China stocks ended at three-month highs on Thursday as subdued industrial data calmed worries over policy tightening, while some positive signs on Sino-U.S. relations also boosted sentiment. ** The blue-chip CSI300 index rose 0.3%, to 5,338.23, its highest closing level since March 3, while the Shanghai Composite Index firmed 0.4% to 3,608.85, its strongest closing since Feb 23. ** Analysts and traders said a series of recent soft economic data helped assuage policy tightening fears which had weighed on valuations of equities and risk appetite. ** Data showed earnings at China’s industrial firms grew at a slower pace in April, with high commodity prices and weaker performance in the consumer goods sector limiting overall profitability from manufacturing. ** “Micro liquidity conditions have improved in the A-share market, with the launch of new mutual funds picking up,” said Yan Kaiwen, an analyst with China Fortune Securities. ** Yan added the strong stock rally would further attract more money inflows via the mutual funds in June, forecasting the Shanghai index to test the 3,800-point level this year. ** So far this week, CSI300 gained 4%, while SSEC advanced 3.5%. ** Foreign inflows continued to prop up the market thanks in part to a buoyant yuan touching a three-year high. ** Investors on Thursday purchased a net 19.5 billion yuan ($3.06 billion) worth of A-shares through the Stock Connect linking the mainland and Hong Kong, according to Refinitiv data. ** The inflows were also partly due to index provider MSCI’s semi-annual review of its China indexes which took effect as of Thursday’s close. ** China and the United States have agreed that the development of bilateral trade is very important, China’s commerce ministry said, adding that both sides exchanged views on issues of mutual concern. ($1 = 6.3776 Chinese yuan renminbi) (Reporting by Luoyan Liu and Andrew Galbraith; Editing by Ramakrishnan M.) Our Standards: The Thomson Reuters Trust Principles.