At the Multi Commodity Exchange, crude oil for delivery in March fell by Rs 32 or 0.50 per cent, to Rs 6,368 per barrel in 4,110 lots.
Similarly, the oil for April delivery moved down by Rs 27, or 0.42 per cent, to Rs 6,370 per barrel in 240 lots.
The trading sentiment turned weak at futures trade after crude oil prices eased in Asian trade as caution set into the market ahead of the release of US economic and stockpiles data, analysts said.