SHANGHAI, May 31 (Reuters) - China stocks eked out gains on Monday and posted their best monthly gain in six as soft domestic factory activity in May eased worries over policy tightening, while a stronger yuan boosted foreign inflows. ** The blue-chip CSI300 index rose 0.2% to 5,331.57, while the Shanghai Composite Index firmed 0.4% to 3,615.48. ** Shenzhen’s start-up board ChiNext added 2.4%, while Shanghai’s tech-focused STAR50 index closed up 4.1%. ** Leading the gains, the CSI new energy index added 4.8%. ** For the month, the CSI300 gained 4.1%, its best since December 2020, while SSEC firmed 4.9%, its best since November 2020. ** For the month, ChiNext advanced 7%, while STAR50 gained 9.1%, its best since June 2020. ** China’s factory activity slowed slightly in May as raw materials costs grew at their fastest pace in over a decade, weighing on the output of small and export-oriented firms. ** Analysts and traders said a recent series of soft data decreased worries over policy tightening, while a stronger yuan helped attract more foreign inflows. ** Investors in the past week purchased a record 46.8 billion yuan ($7.35 billion) worth of A-shares via the Stock Connect linking the mainland and Hong Kong. ** Their net purchasing reached nearly 60 billion yuan in May, according to Refinitiv data. ** “There is relatively ample liquidity in the market, while China’s economy remains in the recovery stage and has yet to entered into a stagflation stage,” said Fu Yanping, a wealth management strategist at China Galaxy Securities. ** Fu said he did not see a continued rally in the market, adding that investors should pocket gains after indexes hit higher levels as the market would remain range-bound going forward. ($1 = 6.3652 Chinese yuan renminbi) (Reporting by Luoyan Liu and Andrew Galbraith; Editing by Ramakrishnan M.) Our Standards: The Thomson Reuters Trust Principles.