SHANGHAI, April 6 (Reuters) - China and Hong Kong stocks fell on Thursday as simmering Sino-U.S. tensions offset fresh evidence of economic recovery, but a sustained rally in artificial intelligence (AI) and semiconductor shares capped losses in China.

** China's blue-chip CSI300 Index fell 0.3% by the lunch break, while the Shanghai Composite Index was little changed.

** Hong Kong's Hang Seng Index fell 0.1%, and the China Enterprises Index lost 0.3%. Tech stocks traded in Hong Kong declined 1.0%.

** China's services activity in March revved up at the quickest pace in 2-1/2 years on robust new orders and job creation and a consumption-led post-COVID recovery, a private-sector survey showed on Thursday.

** But any optimism was counteracted by a flare-up in Sino-U.S tensions as U.S. House Speaker Kevin McCarthy hosted Taiwanese President Tsai Ing-wen in California on Wednesday, and stressed the need to accelerate arms deliveries to Taiwan in the face of rising threats from China.

** An index tracking China's defence stocks rose as maritime authorities in China's Fujian province launched a three-day special patrol and inspection operation in the Taiwan Strait.

** Meanwhile, investors closely monitor the China visits by EU chief Ursula von der Leyen and French President Emmanuel Macron, which could set a course for future relations after years of strained ties.

** China's AI-related stocks continued to rise despite growing bubble concerns following price surges over the past month on the back of the ChatGPT mania.

** The AI index rose 1.1% while China's chipmaking index surged 4.9%. (Reporting by Shanghai Newsroom; Editing by Varun H K)