BEIJING, Dec 18 (Reuters) - Copper prices opened lower on Monday as the U.S. dollar steadied amid uncertainty about the Federal Reserve's interest rate path, although supply headwinds lent some support to the metal.

Three-month copper on the London Metal Exchange was down 0.3% to $8,524 per metric ton by 0143 GMT, while the most-traded January copper contract on the Shanghai Futures Exchange dipped 0.2% to 68,580 yuan ($9,622.29) per ton.

The dollar index held steady after rebounding in the previous session as the New York Fed president said that it's "premature" to speculate about interest rate cuts.

A firmer dollar typically weighs on metal prices as it makes it more expensive to buy the greenback commodity.

However, tightening supply of copper concentrate provided some support to the market.

Fees to process the raw material have fallen by a quarter in less than three months in the Chinese spot market, mainly due to fears of a decline in supply from First Quantum's Cobre mine in Panama.

LME aluminium lost 0.7% to $2,233 a ton, nickel fell 1% to $16,975, zinc slid 0.8% to $2,511.50, lead slid 0.3% to $2,075, and tin shed 0.6% to $25,030.

SHFE aluminium increased 0.7% to 18,865 yuan a ton, nickel was little changed at 132,650 yuan, zinc dipped 0.1% to 20,760 yuan, lead edged up 0.1% to 15,595 yuan, and tin decreased 1.5% to 206,830 yuan.

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($1 = 7.1272 Chinese yuan)

(Reporting by Siyi Liu and Dominique Patton; Editing by Subhranshu Sahu)