NEW ORLEANS (Reuters)—BP P.L.C. will gain access to U.S. government documents that may shed light on the size of the 2010 Deepwater Horizon oil spill in the Gulf of Mexico, a crucial issue in determining the oil company's liability.

According to a Wednesday court filing, the government agreed to produce the documents after BP had accused it two weeks ago of unfairly withholding them because they were privileged.

BP has said the documents may show that an August 2010 estimate of 4.9 million barrels of oil spilled, of which about 800,000 barrels were cleaned up, is too high.

A reduction would lower the maximum civil fine BP could pay under the U.S. Clean Water Act, now estimated as high as $17.6 billion. That law calls for a maximum fine of $1,100 per barrel of oil spilled, or $4,300 if there were gross negligence.

In a filing with the U.S. district court in New Orleans, the government said it will produce 100 documents that BP requested, citing "the importance of this case and the desire of the court to keep this case moving expeditiously."

It said it will work with BP to produce other similar documents, and expects the company to do the same on documents concerning "flow rate" issues at the ruptured Macondo well.

BP, through an outside spokeswoman, declined to comment.

On March 29, BP accused the government of improperly withholding more than 10,000 documents because they reflected policy deliberations.

The London-based company said this decision swept too broadly by keeping factual evidence on the amount of oil discharged under wraps.

In Wednesday's filing, the government said it expects to re-review about 13,000 documents by May 15, and invoke privilege as needed to ensure that decision-making is not impeded.

BP agreed in principle on March 2 to pay $7.8 billion to settle claims by more than 100,000 private plaintiffs for economic, property and other damages.

It still faces potential claims from the government, Gulf Coast states and drilling partners Transocean Ltd. and Halliburton Co.

U.S. District Judge Carl Barbier has scheduled a May 3 meeting with lawyers to discuss how the case should proceed.