FORTUNE — It’s time for BP BP to begin paying damage claims four years after one of the biggest oil spills in U.S. history.

As the oil company seeks to appear before the U.S. Supreme Court over payments it disputes, BP must start doling out hundreds of millions for damage claims from the 2010 spill, the U.S. Court of Appeals in New Orleans ruled. The court rejected the request for a temporary halt on payments to businesses that BP believes would be unfairly included in the $9.2 billion sum, according to a Bloomberg report.

“We are pleased that the court has refused BP’s latest request to further delay claims payments,” wrote Steve Herman and Jim Roy, attorneys for the spill victims, in an email to Bloomberg.

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The payouts had been suspended since last June. By going to the Supreme Court, BP is using the last legal avenue possible to challenge the claims.

In a statement from BP released last Wednesday, the British oil company announced that it is seeking review of “decisions relating to the compensation of claims for losses with no apparent connection to the Deepwater Horizon spill.”

After the explosion sank a Deepwater drilling platform near Louisiana in 2010, 11 workers were killed and 16 others were injured. BP has since paid $12 billion in compensation, along with $14 billion for crisis response and costs associated with the cleanup, according to CNN.