HONG KONG, July 21 (Reuters) - China stocks hit multi-month highs on Monday, led by rare earth and construction sectors, while Hong Kong shares rose as tech stocks rallied following a government rebuke on price wars.

** At the midday break, the Shanghai Composite index .SSEC rose 0.4% to 3,549.89, the highest since last October. China's blue-chip CSI300 index .CSI300 added 0.2% to a seven-month high.

** Leading the gains, the CSI Construction & Engineering Index .CSI399995 jumped as much as 4% after China began construction of a $170 billion hydropower dam in Tibet.

** The rare earth sector .CSI930598 advanced nearly 3% following a Reuters report that Beijing has quietly issued its first 2025 rare earth mining and smelting quotas.

** Positive catalysts from anti-involution policies and strength in the tech sector lifted sentiment, while a solid economic foundation fuelled the market rally that's surprising in its timing yet reasonable, Huatai Securities said.

** Hong Kong's benchmark Hang Seng Index .HSI grew 0.3% after briefly topping the 25,000 level for the first time since February 2022.

** Platform companies Meituan 3690.HK, JD.com 9618.HK and Alibaba 9988.HK rose between 1.8% and 2.8% after Beijing summoned the three and asked them to cool a bruising price war in an ongoing "anti-involution" campaign.

** This came after regulators called for "rational competition" in the auto and food delivery sectors to regulate intense price wars and promote sustainable development, dubbed by investors as an "anti-involution" campaign.

** The biotech sector .HSHKBIO declined 1.4% to pare a nearly 13% rally last week, weighing on gains in Hong Kong.

** Looking ahead, Chinese policymakers are expected to hold the July Politburo meeting in the coming days to discuss economic policies for the second half of this year.

** "They may reiterate their pledge to boost domestic demand and to stabilise exports, employment and the property market" instead of rolling out broad-based, significant stimulus in the near term, analysts at Goldman Sachs said.

** They also anticipate continued policy pledges to regulate disorderly price competition and contain the "involution".

(Reporting by Jiaxing Li in Hong Kong; Editing by Sumana Nandy)

((jiaxing.li@thomsonreuters.com))