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) fell 0.7% to 81,180 yuan ($11,254.84) per metric ton at the midday break, tracking an aggregated 0.8% decline on the London Metal Exchange, while the Chinese markets were closed for a holiday last week.

SHFE zinc shed 0.2% to 23,330 yuan, tin dropped 0.6% to 259,820 yuan, while aluminium rose 0.7% to 20,745 yuan, lead advanced 1.4% to 17,575 yuan and nickel increased 0.4% to 144,590 yuan.

The London Metal Exchange is closed for a public holiday.

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 showed 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.

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DATA/EVENTS (GMT)

0750 France HCOB Services, Composite PMI April

0755 Germany HCOB Services, Composite PMI April

0800 Euro Zone HCOB Services, Composite PMI April

($1 = 7.2129 yuan) (Reporting by Mai Nguyen in Hanoi; Editing by Rashmi Aich)