Shares of American were climbing 5.2% to $11.77, while Boeing was rising 2% to $176.73.
American Airlines has struggled to secure financing for 17 jets it had expected Boeing to deliver this year, according to The Wall Street Journal.
The coronavirus pandemic has led to a sharp drop in air-travel demand and left global airlines fighting to survive, with many unable to afford planes they no longer need.
Airlines will probably lose "an unprecedented $84 billion," Brian Pearce, chief economist for the International Air Transport Association, recently told CNBC.
American said that as of July 1 it had stopped restricting the number of seats sold on flights, dropping the limits on passenger loads implemented as social distancing measures against the coronavirus pandemic.
The airline said it would continue to notify customers and allow them to move to more open flights.
Boeing said in May that it had resumed production of its troubled 737 MAX aircraft, following crashes in Indonesia and Ethiopia last year that killed 346 people. Still, Pearce said he expects a recovery in the second half of 2020.
Last month, Norwegian Air Shuttle told Boeing it would not be moving forward with buying nearly 100 remaining Boeing-built planes and that it was suing Boeing over losses from the grounding of the 737 MAX and issues with engine performance of its Boeing-built 787 Dreamliners.
The Federal Aviation Administration recently said it would begin testing the 737 MAX soon.
American Airlines declined to comment. Boeing said in a statement that "our focus continues to be on working with global regulators on the rigorous process they have put in place to safely return the 737 MAX to commercial service."
"We are not going to comment on discussions with our customers," the statement said. "It is an unprecedented time for our industry as airlines confront a steep drop in traffic. We continue to work closely with our customers to support their operations, while balancing supply and demand with the realities of the market.”