June 11 (Reuters) - Most base metals prices fell on Tuesday, as a weaker yuan reduced the purchasing power of Chinese buyers, while high inventories and weak demand pressured aluminium prices.

Three-month copper on the London Metal Exchange (LME) fell 0.4% to $9,858.50 per metric ton by 0300 GMT, while the most-traded July copper contract on the Shanghai Futures Exchange (SHFE) dropped 2.3% to 79,890 yuan ($11,014.90) a ton.

China's yuan fell to a near seven-month low against the U.S. dollar, as investors returned from a long weekend break to play catch-up with broad greenback strength in overseas markets.

The LME cash copper contract on Monday traded at a $133.14-a-ton discount to the three-month contract, the biggest discount since May 8, indicating that there was no tightness of nearby supply.

LME aluminium eased 0.3% to $2,565 a ton, zinc fell 0.3% to $2,841.50, tin edged down 0.3% at $31,920, while nickel rose 0.8% to $18,025 and lead increased 0.2% to $2,212.

The discount of the LME cash aluminium contract to the three-month contract expanded to $62.44 a ton, the biggest discount since August 2007, after inventories more than doubled in just a month to 1.1 million tons.

"It's a combination of the Rusal deliveries, bad physical demand due to high prices and most probably a pickup in shorts since prices fell recently," said a trader, referring to Russian aluminium inflows into LME warehouses in recent months on lucrative rent deals.

However, share of Russian-origin aluminium have dropped lately, while the share of Indian origin jumped.

SHFE aluminium shed 2% to 20,885 yuan a ton, nickel dropped 2.8% to 139,140 yuan, zinc declined 2.1% to 23,695 yuan, lead fell 0.7% to 18,755 yuan and tin lost 0.8% to 264,240 yuan.

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($1 = 7.2529 yuan) (Reporting by Mai Nguyen in Hanoi; Editing by Eileen Soreng)