Aug 22 (Reuters) -Copper prices fell on Thursday in London, weighed down by a firmer dollar, but falling metal inventories and demand showing signs of improvement limited losses.

Three-month copper on the London Metal Exchange CMCU3 fell 0.3% to $9,232 per metric ton by 0238 GMT, while the most-traded September copper contract on the Shanghai Futures Exchange SCFcv1 advanced 0.2% to 73,870 yuan ($10,352.61) a ton.

The dollar index .DXY edged up 0.2%, rebounding from its lowest in nearly eight months hit on Wednesday, as U.S. interest rate cut hopes weighed. A firmer dollar makes greenback-priced metals more expensive to holders of other currencies.

However, the price fall in metals are limited.

"The macroeconomic backdrop is not looking as gloomy as recently feared. Fundamentals are showing signs of improvement too," said ANZ analyst Soni Kumari, referring to possible output in for copper, aluminium, nickel and zinc.

"Inventories are retreating and contango forward curve is narrowing... suggesting a tighter market. Downstream demand is showing signs of improvement as well for copper and aluminium," she added.

SHFE zinc SZNcv1 climbed as much as 1.7% to 23,780 yuan a ton, its highest since July 18. LME zinc CMZN3 rose to as high as $2,870 a ton, a level unseen since July 17.

Bloomberg reported on Wednesday that Chinese zinc smelters were discussing possible output cuts after tight supplies of concentrates forced spot processing fees into negative territory.

"Chinese smelters are suffering big financial losses now with such low treatment charges and a few smelters that cannot obtain enough concentrates have to cut production," said CRU analyst Dina Yu.

LME nickel CMNI3 fell 0.7% to $16,790 a ton, tin CMSN3 eased 0.1% to $32,650 while aluminium CMAL3 was almost flat at $2,486.50 and lead CMPB3 rose 0.1% to $2,087.

SHFE aluminium SAFcv1 rose 0.5% to 19,850 yuan a ton, tin SSNcv1 increased 0.6% to 265,740 yuan while nickel SNIcv1 fell 1% to 129,630 yuan and lead SPBcv1 shed 0.7% to 17,490 yuan.

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Reporting by Mai Nguyen in Hanoi; Editing by Rashmi Aich

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