The petrol giant says the sum refers to the cost of spill response, containment, relief well drilling, and payments to the Gulf Coast states to speed up their response plans, settlements and federal costs.
However, the final bill is likely to be much higher as the well, which caused the leak, is still pumping at least 5,000 barrels per day of crude into the sea.
Fishermen’s groups have lodged lawsuits for damages and others included people in the tourism industry have complained of losses due to the spill. BP said it would cover all “legitimate” claims for compensation.
It is expected to take some three months to finish work on the first relief well.
Last week, BP declared a 135% surge in first-quarter profits to $5.6bn (£3.8bn), from $2.4bn (£1.6bn) a year ago.