SHANGHAI, June 30 (Reuters) - China stocks bounced higher on Thursday, with major indexes set for their biggest monthly gain in nearly two years, supported by signs of economic recovery and the easing of COVID-19 restrictions, while Hong Kong was largely flat. ** By midday break, Shanghai Composite index rose 1.3% to 3,405.64 points, while blue-chip CSI300 index gained 1.62% to 4,492.2 points.

** Both indexes were set for their best months since July 2020, if gains hold. ** The financial sector sub-index was up 1.15%, the consumer staples sector climbed 2.23%, the real-estate index edged up 0.84% and the healthcare sub-index jumped 3.19%.

** In Hong Kong, the benchmark Hang Seng Index was largely flat at noon, while Chinese H-shares listed in Hong Kong edged up 0.21% to 7,710.91 points.

** The smaller Shenzhen index advanced 1.76%, and the start-up board ChiNext Composite index surged 2.1%.

** Gains across the board came as official data released earlier in the session showed that China's factory and service sectors snapped three months of activity decline in June, as authorities lifted a strict COVID lockdown in Shanghai, reviving output and consumer spending.

** "The worst is perhaps over, but the recovery remains uneven, with industrial production outpacing domestic demand," Citi analysts said in a note. But they pointed out uncertainties around lingering COVID-induced disruptions, weak sentiment and global recession risks.

** China's central bank needs to keep cuts to interest rates and banks' reserve requirement ratio among its policy options while waiting for the economy to bounce back, said Guan Tao, a former senior official at the country's foreign exchange regulator.

** Analysts said hopes for more stimulus measures, including monetary easing, continued to lend support for the markets. "In the early stage of economic recovery, regardless of the pace of growth, monetary policy at least favours an easing bias," said Zhang Jingjing, chief macro analyst at China Merchants Securities. ** The latest easing of coronavirus travel rules combined with other encouraging policy signals have began luring some foreign investors back to Chinese stocks, raising the chances that the market can sustain its bounce after months of heavy selling.

** Official data showed that foreign investors bought 139.15 billion yuan ($20.79 billion) of China stocks this month through the Stock Connect scheme, the most this year.

** Tourism and liquor sectors were among the biggest winners as easing coronavirus restrictions boosted investor sentiment. An index tracking tourism-related companies jumped 4.37% by midday, set to log the biggest weekly gain in nearly two years. ** CSI liquor, a gauge that measures the performance of spirits producers, rose 3.81% on Thursday. Wuliangye Yibin Co Ltd jumped 4.1% to 199.94 yuan, while Kweichow Moutai surged 2.1% to 2,050.1 yuan by lunch break.

($1 = 6.6946 Chinese yuan)

(Reporting by the Shanghai Newsroom; Editing by Sherry Jacob-Phillips)