The recommendation came at the end of the National Transportation Safety Board's investigation of a fatal 2018 accident.Read more
Southwest, the world's largest user of Boeing's 737 Max with 34 jets and dozens more on order, has taken a $175m hit in the second quarter from problems with the plane.
Gary Kelly, chief executive, said: "Our financial and operational performance was remarkably strong considering the impact of the grounding of the Boeing 737 Max 8 aircraft, which reduced operating income an estimated $175m in second quarter, alone.
"Our employees did a heroic job managing approximately 20,000 flight cancellations under operationally difficult circumstances, while delivering excellent customer service."
Talks with Boeing about compensation are yet to be concluded, he said.
BBC Radio 4
American Airlines and Southwest Airlines announced this weekend that they would scrap flights because of the grounding of 737 Max planes.
American Airlines said 115 flights a day would be affected in the coming months by the grounding of the Boeing jets.
Southwest Airlines has cancelled its Max flights to 5 August.
Chris Tarry, aviation expert, told BBC Radio 4's Today programme that it is going to take a considerable period of time for the planes to get back in the air.
They were grounded after the worldwide following fatal crashes involving Ethiopian Airlines and Indonesia's Lion Air.
The story on the American Airlines groundings is here.
Southwest, Delta, and United airlines took to Twitter this morning to apologise for system-wide outages.
Southwest told fed-up passengers: "We're working through some technical difficulties".
Delta had a similar message for tired travellers: "Our team is working diligently to get this resolved and hope to have you on your way shortly".
United Airlines said: "It appears that we are experiencing an outage that is impacting our ability to create release paperwork".
However it looks as if the situation may have been been resolved, though it's not clear how many flights have been delayed - or cancelled - because of the outage.
Southwest just tweeted:
The impact of the grounding of Boeing's 737 Max planes could be having an impact on Southwest Airlines.
The US carrier said its operating revenue per available seat mile - a key measure used to measure the financial performance of airlines - would be less than expected.
It had previously expected a year-on-year rise for the first quarter of between 3%and 4% but lowered this to 2% to 3%.
Its shares were down 2.5% in pre-market trading.
US carrier Southwest Airlines has said it is allowing customers booked on Boeing 737s to change their flights.
In a statement, the airline said: "We are not issuing refunds of non-refundable fares, but we are working with Customers individually who wish to rebook their flight if they want to change their reservation.
"We remain confident in the safety and airworthiness of our fleet of more than 750 Boeing aircraft."
Southwest Airlines says it expects a $60m hit from the US government shutdown.
That's more than the $10m to $15m it had previously expected.
The airline also cut its forecast for revenue per seat.
Herb Kelleher, who co-founded low-cost US carrier Southwest Airlines, has died aged 87.
The company described him as "a pioneer, a maverick and an innovator" who disrupted the airline industry "by making flying both fun and affordable".
He is survived by his wife Joan and three of their four children.