BP PLC agreed to accept criminal responsibility for the 2010 Deepwater Horizon disaster that killed 11 workers and to pay $4.5 billion in fines and restitution, the biggest penalty ever levied by the U.S. Justice Department.

But the oil producer still faces an even costlier battle with the government over civil penalties for the pollution unleashed when the drilling rig exploded in the Gulf of Mexico and caused the worst offshore oil spill in U.S. history.

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