HANOI, May 10 (Reuters) - Copper prices climbed to record high levels in both London and Shanghai markets, as hopes of improved demand and tight supply fuelled sentiment. Three-month copper on the London Metal Exchange touched its all-time high level of $10,660.50 a tonne earlier in the session before easing to $10,628 a tonne, still up 2%, at 0234 GMT. The most-traded June copper contract on the Shanghai Futures Exchange climbed 4.2% to 77,260 yuan ($12,014.24) a tonne, after touching its record high level of 77,540 yuan earlier. Sentiment has been supported since Friday after prices on the LME broke a record high level for the first time since 2011. Bullish investors bet that demand for copper will increase further as the world economy recovers from COVID-19 slumps and as investments into green energy sectors ramped up, while prices were also supported by tight supply in the concentrate market. FUNDAMENTALS * LME aluminium rose 1.2% to $2,571 a tonne and zinc advanced 1.1% to $3,048 a tonne. ShFE zinc hit its highest since March 2008 of 23,030 yuan a tonne, while ShFE aluminium climbed 2.2% to 20,135 yuan a tonne. * A group of 15 key copper smelters in China have agreed to cut their purchases of raw material copper concentrate in 2021 by 8.8% year-on-year, state-backed research house Antaike said, in a bid to boost flagging treatment and refining charges. ADVERTISEMENT * For the top stories in metals and other news, click or MARKETS NEWS * Stocks rose amid speculation that interest rates will remain low for an extended period due to the receding risk of a rapid acceleration in inflation, while oil prices jumped after a cyber attack on a U.S. pipeline operator unnerved markets. DATA/EVENTS (GMT) 0730 UK Halifax House Prices MM April $1 = 6.4307 yuan Reporting by Mai Nguyen; Editing by Rashmi Aich