May 21 (Reuters) - Copper prices rose on Tuesday, hovering around their record highs, as investors took a breather to assess the sustainability of the price rally amid a lack of robust physical demand.

Three-month copper on the London Metal Exchange (LME) edged up 0.1% at $10,902.50 per metric ton by 0710 GMT. Earlier in the session, it fell as much as 1.1% to $10,768, pressured by a firm dollar.

The most-traded July copper contract on the Shanghai Futures Exchange (SHFE) closed up 0.4% at 87,090 yuan ($12,033.16) a ton. The contract lost as much as 1% earlier in the session to 85,860 yuan.

Copper rallied to a record high of $11,104.50 on Monday as a rally triggered by short covering created momentum for speculators and funds to bet on a potential long-term shortage of copper in the green energy transition. The LME contract has risen 27% this year.

However, on the physical market, copper demand is not as strong. The usual premium that Chinese consumers and traders pay to import copper has switched to zero and even fallen below it since mid-May, the lowest since at least 2012.

Meanwhile, copper stocks in SHFE warehouses have been elevated since February and were at 290,376 tons on Friday, up from 33,130 tons at the beginning of the year.

"While supply issues in copper are real, we believe prices are running ahead of fundamentals... Even signs of subdued demand in China have failed to dampen spirits," said ANZ analyst Soni Kumari.

"Momentum can take prices higher further, but we expect prices to consolidate or level off at least until we see Chinese demand turning up," she added.

LME aluminium rose 0.5% to $2,642 a ton, nickel dropped 0.7% to $21,455, zinc was up 0.7% at $3,136.50, lead was nearly flat at $2,341.50 and tin decreased 0.6% to $34,275.

SHFE aluminium edged up 0.1% to 21,095 yuan a ton, tin eased 0.2% to 279,640 yuan, lead fell 0.9% to 18,655 yuan, while nickel increased 1.1% to 157,810 yuan, and zinc advanced 2.6% to 24,810 yuan.

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($1 = 7.2375 yuan) (Reporting by Mai Nguyen in Hanoi; Editing by Mrigank Dhaniwala and Varun H K)