NEW YORK (MarketWatch) -- The oil well at the site of the sunken Deepwater Horizon oil rig continues to leak 1,000 barrels of oil a day into the Gulf of Mexico, according to Mike Abendoff, a spokesman for the joint information center staff handling the accident. BP (BP 59.73, -0.15, -0.25%) is attempting to shut off and contain the leak, which began last week after an explosion and fire caused the Transocean (RIG 89.89, -0.40, -0.44%) rig to sink. BP was leasing the rig from Transocean for oil exploration in the Gulf.