The Supreme Court has declined to take up oil company BP’s challenge to the settlement in its 2010 oil spill in the Gulf of Mexico. (Reuters)

The Supreme Court on Monday refused BP’s challenge to

­a multibillion-dollar settlement arising from the massive 2010 Gulf of Mexico oil spill, declining to hear the company’s case that it is being forced to compensate businesses for losses unrelated to the disaster.

BP had waged a major public relations battle and hired an all-star battalion of lawyers to make the case that federal courts and the claims administrator misread the agreement that sought to settle claims related to the nation’s worst offshore oil spill.

But the Supreme Court without comment declined to review lower-court rulings that rejected BP’s claims . Those courts said the company must abide by an agreement that did not require the kind of proof BP now insists upon.

The terms “are not as protective of BP’s present concerns as might have been achievable . . . but they are the protections that were accepted by the parties and approved by the district court,” Circuit Judge Leslie Southwick wrote in March when a panel of the U.S. Court of Appeals for the 5th Circuit ruled 2 to 1 against BP. “There is nothing fundamentally unreasonable about what BP accepted but now wishes it had not.”

BP was trying to limit the cost of the settlement reached in late 2012. At the time, BP estimated that the deal would cost the company $7.8 billion, but now says the price tag is pushing $10 billion and could climb higher.

The company has made the case in lobbying and full-page ads in The Washington Post and the New York Times that additional costs are resulting from bogus filings approved by claims administrator Patrick Juneau that have enriched unaffected businesses and aggressive lawyers.

The “business economic loss” settlement accounts for only part of the billions of dollars BP has had to pay in fines, cleanup costs and settlements related to the 2010 oil rig explosion off the Louisiana coast that killed 11 people and discharged 200 million gallons of oil. The company said it had set aside $42.5 billion to, in its words, “make things right.”

The company agreed to the settlement to hasten the litigation process and limit its expenses, but Washington lawyer Theodore Olson told the Supreme Court in the company’s brief that decisions by lower courts and Juneau had defeated the purpose.

“The class yokes together many claimants that suffered ­spill-related losses with numerous others whose alleged losses are entirely unrelated to the spill, thereby awarding damages without any connection to the theory of liability,” Olson wrote.

Among several examples, he said, was a $3.5 million award to an excavation company in Alabama, even though its revenue drop during the relevant period was because of a decision to sell assets in 2009, before the spill occurred.

But lawyers for the class of claimants covered by the agreement said BP simply had “buyer’s remorse.” Before the lower courts, the company had explicitly agreed to hypothetical cases almost identical to the ones it now criticizes, these lawyers said.

Independent audits have shown that Juneau has correctly processed more than 99 percent of the claims he has received.

“Today’s ruling is a huge victory for the Gulf, and should finally put to rest BP’s two-year attack on its own settlement,” the lead attorneys for the class of affected businesses, Stephen J. Herman and James P. Roy, said in a statement. “With the high court’s rejection of BP’s attempts to rewrite history, Mr. Juneau can get on with the business of processing and paying eligible claims.”

BP said it remains concerned “that the program has made awards to claimants that suffered no injury from the spill — and that the lawyers for these claimants have unjustly profited as a result,” said company spokesman Geoff Morrell. “On behalf of all our stakeholders, we will therefore continue to advocate for the investigation of suspicious or implausible claims and to fight fraud where it is uncovered.”

The case is BP Exploration v. Lake Eugenie Land & Development.