"We have concluded that a merger with American, while they are undergoing their bankruptcy restructuring, represents a unique opportunity that we should not ignore," Parker wrote.
Parker said a merged airline would save at least 6,200 of 13,000 jobs that would be lost under American's go-it-alone plan.
The unions oppose American's plan to eliminate the 13,000 union jobs and cut labor costs to return to profitability. American is seeking to throw out contracts with the unions that govern pay, benefits and work rules, and impose its own terms on employees.
US Airways and the unions said they had agreed on terms for collective bargaining agreements if there is a merger between the airlines.
The three unions - the Transport Workers Union, the Association of Professional Flight Attendants, and the Allied Pilots Association - said they supported a merger as "the best strategy and fastest option to complete the restructuring of American Airlines, enabling it to exit the Chapter 11 bankruptcy process and restore American Airlines to a preeminent position in the airline industry."
A merged company would keep the American name and Dallas-Fort Worth headquarters. US Airways is headquartered in Tempe, Ariz.
American Airlines' chief executive, Tom Horton, has argued that the best future for American is as a stand-alone company. The company on Thursday reported a $1.7 billion loss for its first quarter.
American is scheduled to begin hearings Monday, during which it will seek to have a bankruptcy court judge throw out its labor contracts.
American said "statements of nonbinding support from union leaders for alternative proposals are no coincidence given the timing" of the Monday hearing.
"These statements do not in any way alter the company's commitment to pursue our business plan or our focus on moving steadily through the court-supervised restructuring process to create a profitable, growing industry leader," American said in a statement.
American has a court-mandated exclusive right until at least Sept. 28 to create its own plan. The judge could extend that period for up to eight months.
The unions hold three of the nine seats on the committee of unsecured creditors in the bankruptcy case of American's corporate parent, AMR Corp. The committee can ask the judge to review the company's exclusive right to present its plan, and if the judge agreed, it could open the way for a merger bid.
US Airways, which emerged from bankruptcy in a merger with America West in 2005, has been seeking a new merger partner for several years. The airline is still digesting the effects of its earlier merger, unable so far to reach contract agreements with the unions that represented the premerger pilots and flight attendants of the two airlines.
Pilots and flight attendants from the two premerger airlines still fly separate planes under separate contracts.
"Seven years later, that deal still isn't done," said the union leaders representing US Airways flight attendants.
"A contract for flight attendants at US Airways must be completed prior to any new merger deal," said the union leaders, Deborah Volpe and Mark Gentile, in a statement Friday. "There is a small window of opportunity for US Airways management to get this right."
US Airways is the dominant carrier at Philadelphia International, carrying nearly 70 percent of the airport's passengers on more than 400 daily departures and arrivals. American, with 16 daily departures, is the fourth-largest carrier at the airport, with 3.6 percent of the market.
Mark Gale, chief executive of the airport, was unavailable to comment on the possible local impacts of the proposed merger, airport spokeswoman Victoria Lupica said. Philadelphia deputy mayor Rina Cutler, who oversees operations at the city-owned airport, also was out of town Friday.
Nationally, US Airways is the fifth-largest airline, in terms of passengers carried, and American is the third-largest. A merger would return the new American Airlines to its former status as the world's largest airline.
US Airways has a history of making plays for larger airlines - twice for United Airlines in 2008 and 2010, after which United tied the knot with Continental, and once in 2007 for then-bankrupt Delta, which merged instead with Northwest.
Any merger plan between American and US Airways would have to be approved by the bankruptcy court and American's creditors committee and board of directors. A merger could also face antitrust challenges.
Contact Paul Nussbaum at 215-854-4587 or firstname.lastname@example.org.