Copper futures for August fell Rs 2.85, or 0.21%, to Rs 406.40 per kg in 339 lots.
At the Multi Commodity Exchange (MCX), the June contract traded lower by 60 paise, or 0.15%, to Rs 402 per kg in 5,370 lots.
Prices fell as speculators offloaded their positions.
On the London Metal Exchange (LME), copper fell 1.1% to $7,275.25 a tonne on demand concerns on speculation that inflation may accelerate in China, curbing further stimulus.