Jets are parked on runway 28 at the Pittsburgh International Airport on March 27, 2020 in Pittsburgh, Pennsylvania. Due to decreased flights as a result of the coronavirus (COVID-19) pandemic, close to 70 American Airlines planes are being stacked and parked at the airport.

American Airlines apologized to its pilots on Wednesday after mistakenly offering thousands of aviators voluntary leave options as part of the company's effort to cut costs to fight the coronavirus's toll on travel demand.

American had "either by miscalculation or miscommunication wrongly indicated" that a minimum of 1,200 pilots who fly Airbus A320 and Boeing 737 narrow-body aircraft could take short-term leave, according to an email to pilots from Kimball Stone, American's senior vice president of flight operations, which was reviewed by CNBC.

"The proffer for short term leaves ... ended yesterday morning, and as we began the award process we discovered that we could offer nowhere near that number of leaves based upon the current April schedule. In fact, Manpower Planning did not believe we would be able to accommodate any A320 or B737 leaves for the month of April," he said.

American did not immediately respond to a request for comment.

American and competitors like Delta, United and others are urging as many employees as possible to take either unpaid leave or partially paid leave in a bid to stem costs. COVID-19 and harsh measures to stop the spread of the virus such as stay-at-home orders and advisories, have sent air travel demand down at the fastest pace on record.

Just 146,348 people were screened at U.S. airports on Tuesday, a nearly 93% decline from a year earlier, according to the Transportation Security Administration.

Congress has approved $58 billion in aid for U.S. passenger and cargo carriers, of which American estimates it will receive $12 billion. The relief package includes $25 billion in grants for carriers if they do not furlough or cut the pay rates of their employees through Sept. 30.

"In other times this may have been just a drop in the bucket but in this critical time when every dollar counts, we're unable to process why they couldn't get this done," said Dennis Tajer, an American 737 captain and spokesman for the Allied Pilots Association, which represents American's some 15,000 pilots.

Fort Worth, Texas-based American, which had close to 134,000 full-time equivalent employees as of the end of last year, earlier this week began offering its nonpilots partially paid voluntary leave to entice more workers to take that option.

Roughly two-thirds of American pilots fly narrow-body planes like the A320 and Boeing 737, according to their pilot union. As it has already cut most of its international service, a move other airlines have also made, many pilots of larger aircraft have been offered voluntary leaves.

"To those of you that selflessly volunteered to leave early ... and reduce the cost to our airline in desperate need of relief, I once again apologize," wrote Stone. "To those who are willing to sacrifice with shorter term leaves that have yet to materialize, I also want to extend my apologies. I know the delay and the change in expectations breaches the trust that our Flight Department has so carefully attempted to build over the past few years. We will do what we can to make it right."

An added wrinkle: pilots who will be awarded leave received schedules that didn't reflect that, but the airline has resolved that glitch, American said.