One day after American Airlines reported mixed results in its third quarter, Parker doubled down on his belief that Boeing should be responsible for shortfalls related to the worldwide grounding of the 737 Max jet model following two fatal crashes.
American's fleet includes 24 of the jets, and the carrier was in line earlier this year to order 76 more from Boeing.
"The reality is this: We've already borne all sorts of damages to our customers, to our team and to our shareholders," he said in a "Mad Money" interview with Jim Cramer. "Certainly the shareholder piece should be borne by the Boeing shareholders, not the American Airlines shareholders."
In July, the Fort Worth-based airline said the 737 Max grounding, which was blamed on faulty software, forced the company to cancel about 115 flights a day. The halting of 737 Max flights across the airline industry has reportedly cost nearly $1 billion. American Airlines estimates that its full-year profit took a $540 million hit from the trouble.
In July, Boeing took a $5.6 billion pre-tax charge in the second quarter due to the 737 Max grounding.
"While we wouldn't comment on private discussions with our customers, we sincerely regret the impact this has had on their business and on their passengers. We continue to work to support them and will deal with the impact individually, customer by customer," Boeing Communications Director Chaz Bickers told CNBC in an email.
Parker told Cramer that the two parties have held "preliminary talks" and that Boeing agreed the airline's concerns were fair.
An Indonesian investigation into the October 2018 crash of a Lion Air 737 Max jet that killed 189 people, which followed another crash involving the same plane model and killed 157 people in Ethiopia, concluded that the plane needed better cockpit design. Other investigations into the airplane are still pending.
It's "hard to have final negotiations until you know what the real damages are, and we don't know what the real damages are until the aircraft is back flying again," Parker said. "So that's what's more important, of course, but I do feel good about the fact that once we are able to get down to brass tax that they will come to the table and be prepared to do what's right."
Regulators have yet to clear the jets to fly again, and Boeing's software changes to the flight-control system have not been approved.
American Airlines pilots, however, will be ready to fly again when the time comes, Parker said.