(Reuters) - BP Plc has accused the U.S. government of withholding evidence that may show the 2010 Deepwater Horizon oil spill in the Gulf of Mexico was smaller than federal officials claimed, a key issue in determining the oil company's liability.

A reduction in the size of the spill would lower the maximum civil fine BP could be forced to pay under the U.S. Clean Water Act, a sum now estimated as high as $17.6 billion.

The government is one of many plaintiffs suing BP over the April 20, 2010 explosion of the Deepwater Horizon drilling rig, which killed 11 workers and triggered the largest U.S. offshore oil spill.

In a filing late on Thursday with the U.S. district court in New Orleans, BP said more than 10,000 documents the government is refusing to turn over "appear to relate to flow rate issues" at the company's ruptured Macondo well.

BP said the documents, which the government considers privileged because they reflect policy deliberations, may show that an August 2010 estimate that 4.9 million barrels of oil spilled from the well is too high.

"The United States' invocation of the deliberative process privilege here sweeps too broadly," because it shields evidence concerning "a factual issue, namely, the amount of oil discharged," wrote Don Haycraft, a lawyer for BP.

"Fundamental fairness" requires that BP get access to this evidence for its defense, he added.

Wyn Hornbuckle, a U.S. Department of Justice spokesman, declined to comment.

In an order dated Friday, U.S. Magistrate Judge Sally Shushan directed BP and the government to meet over the next couple of weeks to try to resolve disagreements over some of the challenged evidence.

The Clean Water Act calls for maximum fines of $1,100 per barrel of oil spilled or $4,300 if there were gross negligence.

Assuming 4.1 million barrels were spilled and not cleaned up as the government contends, BP could face a maximum $17.6 billion fine if there was gross negligence.

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

BP has calculated its legal and cleanup costs to be roughly $43 billion. The company is based in London.

The settlement with private plaintiffs put a potentially year-long trial over the spill on indefinite hold. The size of the spill was among the issues to be determined.

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

The case is In re: Oil Spill by the Oil Rig "Deepwater Horizon" in the Gulf of Mexico, on April 20, 2010, U.S. District Court, Eastern District of Louisiana, No. 10-md-02179.

(Reporting By Jonathan Stempel in New York; Editing by Andre Grenon and Steve Orlofsky)