Qatar Airways is attempting to buy a 10 percent stake in American Airlines. American said Thursday that the bid was unsolicited, but that there have been conversations between the CEOs of both airlines.

DALLAS — Qatar Airways wants to buy 10 percent of American Airlines, a move cloaked so heavily in international trade and politics that American’s CEO finds it puzzling.

American has tried to convince two successive U.S. administrations that Qatar and two other state-owned Middle Eastern carriers get illegal subsidies from their governments. Qatar has fought back in the increasingly nasty dispute. Now Qatar is suffering because its nation is under blockade by its Arab neighbors, who have closed their airspace to the carrier.

On Thursday, Qatar said it plans to buy an initial stake of up to 4.75 percent American’s stock. American said Qatar CEO Akbar Al Baker told American CEO Doug Parker that he wants to acquire about 10 percent of the airline’s stock, which would cost about $2.4 billion. The two men met secretly in early June at an airline-industry conference in the Mexican resort town of Cancun.

Although the two airlines are on opposite sides of a trade fight, they sell seats on each other’s flights and cooperate as members of the same alliance of global carriers.

Qatar said in a statement that it hopes to continue that relationship. It said it sees a “strong investment opportunity” in American, and would be merely a passive investor with no role in American’s management or operations.

American, the world’s biggest airline, said Qatar’s bid was unsolicited, and Parker belittled it.

“We aren’t particularly excited about Qatar’s outreach,” the CEO wrote in a memo to American employees. He said the move was “puzzling” given American’s ongoing fight over claims that Qatar, Emirates and Etihad Airways receive unfair government subsidies — a fight he vowed to keep pursuing.