The oil company said in court documents Tuesday in Louisiana that it has yet to deny any claims. Many of the claims are from fishermen and shrimpers.
BP said 25,000 claims have been submitted and more than 12,000 payments have been made so far.
BP is trying to block an attempt by some fishermen to get a federal judge to oversee the claims process.
BP says the 1990 Oil Pollution Act gives the Coast Guard oversight responsibilities.
BP and other companies involved in the Deepwater Horizon rig disaster have been targeted by more than 130 lawsuits. BP says people who accept claims do not waive rights to sue.