SHANGHAI, July 4 (Reuters) - China stocks rose slightly on Monday, lifted by the newly launched cross-border investment scheme ETF Connect, but gains were capped by signs of rising COVID-19 infections.

In Hong Kong, equities fell as airline stocks weighed on key indexes.

** China's blue-chip index CSI300 rose 0.2% by the midday break, while the Shanghai Composite Index gained 0.1%. In Hong Kong, the benchmark Hang Seng Index fell 0.6%.

** Investors in China and Hong Kong started trading exchange-traded funds (ETFs) in each other's markets on Monday, but more money will likely flow into mainland markets initially under ETF Connect.

** With just four Hong Kong-listed ETFs qualified — compared with 83 eligible products traded in Shanghai and Shenzhen — the benefits are sharply skewed toward funds that invest in China-listed shares.

** But risk appetite in China was curbed by signs of a possible flare-up in COVID-19 outbreaks.

** Parts of eastern China are running fresh rounds of mass COVID-19 testing, as the country faces new waves of infections while recovering from impact of the spring outbreaks that hit Beijing and Shanghai.

** Daily numbers of locally transmitted infections in mainland China increased to more than 300 over the weekend, compared with a few dozens in late-June.

** An index tracking China's healthcare stocks surged nearly 4%, but tourism and transport stocks shares fell sharply.

** China's "Big Three" state airlines tumbled in both China and Hong Kong, after they pledged on Friday to buy a total of almost 300 Airbus jets, the biggest order by Chinese carriers since the start of the pandemic.

** Hong Kong shares of Air China slumped 7.5% by the lunch break, on track for their worst day since March.

** Shares of China Southern Airlines and China Eastern Airlines also fell sharply. (Reporting by Shanghai Newsroom; editing by Uttaresh.V)