The U.S. Supreme Court rejected appeals from BP Plc and Anadarko Petroleum Corp., leaving intact a ruling that opens the companies to potentially billions of dollars in fines for the 2010 Gulf of Mexico oil spill.

The federal government is seeking as much as $13.7 billion in civil fines from BP and more than $1 billion from Anadarko. The offshore spill, caused by the explosion of BP’s Deepwater Horizon oil rig, was the largest in U.S. history, releasing millions of barrels of oil into the Gulf.