May 6 (Reuters) - Shanghai copper prices fell on Monday, tracking losses in London, amid a firmer dollar and a lack of clear demand improvement from the troubled Chinese property market.

The most-traded June copper contract on the Shanghai Futures Exchange (SHFE) closed down 0.6% to 81,300 yuan ($11,268.35) per metric ton, tracking an aggregated 0.8% decline on the London Metal Exchange. Chinese markets were closed for a holiday last week.

The London Metal Exchange is closed for a public holiday on Monday.

The dollar index rebounded, after hitting a three-week low in the previous session. A firmer dollar makes greenback-priced metals more expensive for holders of other currencies.

Copper prices have been supported by a potential cut of smelters' output due to limited mine supply. However, data has not reflected any large cut and smelters with long-term raw material supply contracts are less likely to do so soon.

"The (copper) smelting profit of long-term orders still remains above 1,700 yuan a ton, so the willingness of companies with long-term orders to actively reduce production may be relatively limited," said Huatai Futures in a report.

Despite the Chinese real estate sector showing no sign of bottoming out, steady demand from the power, electric vehicles and home appliances sectors contributed to a generally good end-user copper demand, Huatai analysts said in the report.

SHFE zinc shed 0.3% to 23,305 yuan, while tin rose 0.2% to 261,900 yuan, aluminium rose 0.7% to 20,745 yuan and nickel increased 0.8% to 145,040 yuan.

SHFE lead closed up 2.4% at 17,740 yuan. Earlier in the session, it hit 17,750 yuan, the highest since July 2018.

Lead inventories in warehouses tracked by SHFE fell to 48,321 tons on April 26, the lowest since Feb. 8, the latest exchange data on LSEG showed.

A trader said tightness of lead ingots in China caused the price jump on Monday.

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