Unions have called on Parker to tie employee compensation to the company's performance, but Parker has opposed profit-sharing, practiced by Delta Air Lines, United Airlines and Southwest Airlines.
"There are many ways to share success, but when it comes to compensation, we believe it is best to reward (workers) with industry leading wage rates not lower wages supplemented by compensation that varies with airline profitability," he wrote in the letter, obtained by Reuters.
The pay increases show how seriously American views labor relations, which have often emerged as a stumbling block in other airline merger deals, as it joins its operations with US Airways a year into the carriers' merger.
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Hourly rates for flight attendants will be seven percent higher than those at Delta or United, Parker said in the letter. A separate letter from the airline cited an hourly rate of $24.18 for first-year flight attendants.
Yet the announcement also placed American's other workers under pressure to conclude contracts, a prerequisite for their raises. The carrier hopes to avoid the fate of other merged airlines that struggled for years to reach deals for all their workers.
Pilots are the next group up for a contract, and the company said in a third letter Tuesday that it had ended negotiations with them, leaving them to choose between a final offer or arbitration as early as February 2015.
The letter added that if pilots accept the offer prior to Jan. 3, higher pay rates would be effective retroactively as of Dec. 2, 2014, rather than after the agreement.
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The company's proposal would raise pilots' pay about 23 percent upon signing and then three percent for the next two years, compared to smaller gains they would get under an arbitrated contract, the company said in the letter.
The airline has also proposed various changes to work rules, some of which have been sticking points in the negotiations.
The Allied Pilots Association, which represents American's pilots, said its board will convene on Jan. 2 and 3 to decide a course of action.