* Shanghai shares add 0.7%, blue-chips up 0.9%
* Policy support, recovery hopes aid sentiment - Everbright Securities
* China fights most aggressive return of COVID-19 cases in months
* President Xi Jinping to speak 0900 GMT at AIIB meeting
HONG KONG, July 28 (Reuters) - Chinese shares rose the most in a week on Tuesday on signs of a recovery in the world's second largest economy, but Sino-U.S. tensions and fresh flare-ups of coronavirus cases capped the rise.
** At the close, the Shanghai Composite index was up 0.7% at 3,227.96. The blue-chip CSI300 index had gained 0.9%. Both indexes saw the highest single-day rise since July 20. ** CSI300's real estate index ticked up 0.7% and the healthcare sub-index fell 0.2%. ** The smaller Shenzhen index added 1.4% and the start-up board ChiNext Composite index rose 1.3%. The new tech-focused STAR 50 index gained 1.9%.
** Investors on Tuesday focused on signs of an economic recovery from the record slump earlier this year. This week, China reported strong growth in June industrial profits, which rose at their fastest pace in over a year.
** "The relatively high pressure on employment and the constant change in coronavirus pandemic mean policy will not rapidly tighten, and Sino-U.S. frictions will not change the trend of profits recovering in the second half," analysts at Everbright Securities said in a note.
** China reported 68 new coronavirus cases for July 27, up for a fourth consecutive day. The country is battling the most aggressive return of COVID-19 in months, driven by infections in the far western region of Xinjiang and a separate flare-up in the northeast.
** Investors will be watching Chinese President Xi Jinping's speech at a meeting of the Asian Infrastructure Investment Bank (AIIB), scheduled to start at 0900 GMT.
** The Shanghai stock index is up 5.8% and the CSI300 has risen 11.5% so far this year. ** About 28.94 billion shares traded on the Shanghai exchange. The volume in the previous trading session was 29.93 billion. (Reporting by Noah Sin; Editing by Vinay Dwivedi)