Updates with closing prices

HONG KONG, June 3 (Reuters) - China and Hong Kong shares edged up on Tuesday, as banking stocks hit record highs and automakers rebounded, though investors remained cautious ahead of key developments later in the week.

** At the close, China's blue-chip CSI300 index .CSI300 gained 0.3%, while the Shanghai Composite index .SSEC advanced 0.4%, both recovering from earlier losses.

** Banking stocks led onshore markets higher, with the CSI Banks Index .CSI399986 rallying 2% to a record high. Chip stocks also strengthened, with the CSI Semiconductor Index .CSI931865 adding 1.4%.

** In Hong Kong, the Hang Seng China Enterprises Index .HSCE tracking mainland companies rose 1.9% to bounce back from a one-month low. The city's benchmark Hang Seng Index .HSI added 1.5%.

** Car makers listed in the city bounced, taking a breather from the recent sell-off triggered by a price war at home. The Hang Seng Automobile Index .HSAMI jumped 2.4%, with Li Auto 2015.HK surging 5.8% and BYD 1211.HK climbing 3.9%.

** On the data front, China's factory activity in May shrank for the first time in eight months, a private-sector survey showed on Tuesday, indicating U.S. tariffs are now starting to directly hurt the manufacturing superpower.

** U.S. President Donald Trump and Chinese leader Xi Jinping will likely speak this week, White House press secretary Karoline Leavitt said on Monday, days after Trump accused China of violating an agreement to roll back tariffs and trade restrictions.

** "A likely return of market volatility in June" is expected due to tariff policy uncertainties and lingering fundamental headwinds seen in macroeconomic data, according to a China equity strategist at Daiwa Capital Markets Hong Kong.

** "We reiterate our cautious market views as a market rebound since mid-April may have already factored in a 'good outcome' of the trade war," he wrote in a note.

(Reporting by Jiaxing Li in Hong Kong; Editing by Rashmi Aich)

((jiaxing.li@thomsonreuters.com; +852 63358304))