SHANGHAI, July 5 (Reuters) - China and Hong Kong stocks closed roughly flat on Tuesday as concerns over the worsening COVID-19 situation offset optimism from recovering services activities in the country.

** The blue-chip CSI300 index .CSI300 ended down 0.1% at 4,489.54, while the Shanghai Composite Index .SSEC ended flat, at 3,404.03 points.

** Sentiment in China was curbed by signs of a flare-up in COVID-19 infections, despite data showing China's services activity snapped three months of decline in June and grew at the fastest rate in almost a year.

** The total number of domestically transmitted cases jumped to 173 from 27 on a seven-day moving average basis, and the number of cities under lockdown or partial lockdowns doubled, Nomura said in a note.

** "Over the past week, the COVID-19 situation has clearly worsened," wrote Ting Lu, Nomura's chief China economist. "Another wave of Omicron could prompt a return to a downswing phase, even though the timing of such an occurrence is uncertain."

** Although the Caixin services PMI bounced back to the expansionary zone, "the highly uncertain COVID-19 development still poses persistent pressures on the future recovery of the service sector, which calls for sustained and targeted policy support," HSBC wrote on Tuesday.

** Tourism .CSI930633 and food & beverage shares fell in China, but steel .CSI930606 , resources .CSI000805 and infrastructure stocks .CSI000950 rose.

** Sourced told Reuters on Tuesday that China will set up a state infrastructure investment fund worth 500 billion yuan ($74.69 billion) to spur infrastructure spending and revive a flagging economy.

** In Hong Kong, healthcare .HSCIH and energy shares .HSCIE rose, but financials and property sectors fell.

** Hong Kong-listed shares of WuXi Biologics 2269.HK jumped 6.5%, on news that the Chinese company is a step closer to being taken off a U.S. trade black list.
Reporting by Shanghai Newsroom