Three-month LME zinc drifted down in Asia after jumping more than 3 percent the previous day, but sentiment stayed bullish due to tight inventory levels.
The most active January copper contract on Shanghai Futures Exchange closed the morning session down at 62,520 yuan a tonne, from Monday's close of 62,550 yuan.
"It is still very hard to find a direction for Shanghai copper in a short period," said Pang Ying, a senior analyst at Minmetals Star Futures in Shenzhen.
"Copper supplies in China will be in an uptrend this month due to stronger domestic prices compared with the LME metal, which lead to depressed prices."
Spot Shanghai copper prices were between 64,400 and 64,700 yuan, down 350 yuan from Monday.
London Metal Exchange copper futures prices drifted down in Asia compared with Monday's close.
By 0350 GMT, the three-month LME copper futures contract was quoted at $6,780/6,800 per tonne, compared with Monday's London kerb close of $6,840.
Traders said the market is watching whether it could hold around $6,400-$6,500 -- the lows reached in June.
"Chinese prices were somewhat supported, but active buying is limited as fundamentals are not strong because of increasing supplies," said a trader at a Japanese trading house.
"But copper should be generally supported from here as other base metals such as zinc, lead and nickel are bullish."
Sentiment for copper has been bearish after it lost around $2,000 since its peak in May at $8,800.
Rising LME copper inventories also prevented investment funds from buying copper heavily.
LME copper warehouse stock rose 2,050 tonnes to 158,025 tonnes on Monday. They have gained about 44 percent from a month ago.
Still, traders were careful about selling copper heavily due to the possibility of labour strikes at copper mines.
On Saturday, about 300 workers from three smaller unions at Chile's Codelco Norte, the giant state-owned copper miner's largest division, voted to accept a three-year contract offer, although larger unions were still negotiating.
The three largest unions at Codelco Norte, comprising nearly 6,000 workers, have until December 31 to reach a deal with the company or go on strike.
The most active January Shanghai aluminium futures ended the morning session up at 19,910 yuan a tonne, from Monday's close of 19,770 yuan.
Other LME metals prices were lower to little changed from their London closes, but zinc lead and nickel were well supported by strong fundamentals.
Three-month LME zinc was quoted down at $4,130 per tonne against Monday's kerb close of $4,169.
Zinc closed over 3 percent higher on Monday as LME stocks were diminished.
Zinc stocks extended their 17-month fall to 90,400 tonnes, their lowest since 1991, down from their peak in 2004 at 783,500.