WASHINGTON — For nearly four years, American taxpayers have been footing the bill for a chunk of the Saudi-led air campaign in Yemen — the gas for many of the Saudi warplanes flying combat missions and the jets that provide the midair refueling.

Now the Pentagon is correcting this accounting error, and has sent Saudi Arabia and its main partner, the United Arab Emirates, a bill for those overdue charges: about $331 million.

Specifically, the Pentagon is seeking about $36.8 million for jet fuel and $294.3 million for flight hours by American refueling aircraft, Cmdr. Rebecca Rebarich, a Pentagon spokeswoman, said on Thursday.

“Due to errors in accounting by the Pentagon, the United States had not properly charged Saudi Arabia and the United Arab Emirates for those services,” Senator Jack Reed of Rhode Island, the senior Democrat on the Armed Services Committee, said in a statement.